Vectorin physics, a quantity that has both magnitude and direction. Although a vector has magnitude and direction, it does not have position. That is, as long as its length is not changed, a vector is not altered if it is displaced parallel to itself. In contrast to vectors, ordinary quantities that have a magnitude but not a direction are called scalars. For example, displacementvelocityand acceleration are vector quantities, while speed the magnitude of velocitytime, and mass are scalars.
To qualify as a vector, a quantity having magnitude and direction must also obey certain rules of combination. Geometrically, the vector sum can be visualized by placing the tail of vector B at the head of vector A and drawing vector C —starting from the tail of A and ending at the head of B —so that it completes the triangle.
Quantities such as displacement and velocity have this property commutative lawbut there are quantities e. The other rules of vector manipulation are subtraction, multiplication by a scalar, scalar multiplication also known as the dot product or inner productvector multiplication also known as the cross productand differentiation.
There is no operation that corresponds to dividing by a vector. See vector analysis for a description of all of these rules. Although vectors are mathematically simple and extremely useful in discussing physics, they were not developed in their modern form until late in the 19th century, when Josiah Willard Gibbs and Oliver Heaviside of the United States and England, respectively each applied vector analysis in order to help express the new laws of electromagnetism, proposed by James Clerk Maxwell.
Info Print Cite. Submit Feedback. Thank you for your feedback. Vector physics. See Article History. Get exclusive access to content from our First Edition with your subscription. Subscribe today. Learn More in these related Britannica articles: scalar.
Scalara physical quantity that is completely described by its magnitude; examples of scalars are volume, density, speed, energy, mass, and time.
Other quantities, such as force and velocity, have both magnitude and direction and are called vectors. Scalars are described by real numbers that are usually but not necessarily positive. Displacementin mechanics, distance moved by a particle or body in a specific direction. Particles and bodies are typically treated as point masses—that is, without loss of generality, bodies can be treated as though all of their mass is concentrated in a mathematical point.
In the figure, A is the…. Velocityquantity that designates how fast and in what direction a point is moving.
A point always moves in a direction that is tangent to its path; for a circular path, for example, its direction at any instant is perpendicular to a line from the point to the centre of…. History at your fingertips. Sign up here to see what happened On This Dayevery day in your inbox! Email address.Free body diagrams are used to describe situations where several forces act on an object. Vector diagrams are used to resolve break down a single force into two forces acting at right angles to each other.
A free body diagram models the forces acting on an object. The object or 'body' is usually shown as a box or a dot. The forces are shown as thin arrows pointing away from the centre of the box or dot. Free body diagrams do not need to be drawn to scale but it can sometimes be useful if they are. It is important to label each arrow to show the magnitude of the force it represents. The type of force involved may also be shown.
Weight and reaction force for a resting object:. Drawing of situation. Free body diagram. Weight, reaction force and friction for an object moving at constant speed down a hill:. Weight, upthrust, thrust and air resistance for an accelerating speedboat:.
A box is at rest on a table. Draw the free body diagram for this situation. A trolley is being pulled along a rough surface at a constant speed. The resultant vector for two vectors at right angles to each other can be worked out using a scale diagram, or using a calculation.
In the diagram below, two velocities are at right angles to each other. If the diagram is drawn to scale like this, the magnitude of the resultant vector can be found by measuring the length of the diagonal vector arrow.
Pythagoras' theorem can be used to calculate the resultant vector. In any right-angled triangle, the square of the longest side is the sum of the squares of the other two sides. This can be written in the formula:. This is where c is the longest side. Free body diagrams and vector diagrams - Higher Free body diagrams are used to describe situations where several forces act on an object.
Free body diagrams A free body diagram models the forces acting on an object. Representing an object in a free body diagram as a box or a dot Free body diagrams do not need to be drawn to scale but it can sometimes be useful if they are. Examples of free body diagrams Weight and reaction force for a resting object: Drawing of situation.Hot Threads.
B Thread starter Indranil Start date Jul 20, According to the vector definition, the vectors have both the direction and magnitude such as displacement vectors which should possess arrows on the top of them because they have displacement so they express a direction. On the other hand, position vectors are stationary, they do not have any displacement so why do they possess arrows on the top of them? Could you explain, please?
Insights Author. They are the displacement of the origin of the coordinate system, resp. ZapperZ Staff Emeritus. Science Advisor. Education Advisor. Indranil said:.
ZapperZ said:. If you ask me "where is the ball? No, because if it is 3 meters away from me, it could be 3 meters away in any direction! If I say, it is 3 meters way in THAT direction and I pointthen you look at the direction that I'm pointing, and the intersection of that and the circle is the location of the particle. I've just given you the location in plane-polar coordinates. I could have easily given it to you in cartesian coordinates.
And by doing that, I've defined a position vector! It has nothing to do with whether something is stationary or moving. Chestermiller Mentor. We represent all vectors with arrows over them to distinguish them from scalars.
Another way of doing this is to represent vectors using boldface, rather than with arrows over them.Vector Basics Force is one of many things that are vectors. What the heck is a vector? Can you hold it? Can you watch it? Does it do anything?
Well, not really. A vector is a numerical value in a specific directionand is used in both math and physics. The force vector describes a specific amount of force and its direction. You need both value and direction to have a vector. Very important. Scientists refer to the two values as direction and magnitude size.
The alternative to a vector is a scalar. Scalars have values, but no direction is needed. Temperature, mass, and energy are examples of scalars. When you see vectors drawn in physics, they are drawn as arrows. The direction of the arrow is the direction of the vector, and the length of the arrow depends on the magnitude size of the vector.
Real World Vectors Imagine a situation where you're in a boat or a plane, and you need to plot a course. There aren't streets or signs along the way. You will need to plan your navigation on a map. You know where you're starting and where you want to be. The problem is how to get there. Now it's time to use a couple of vectors. Draw the vector between the two points and start on your way.In physics, when you have a vector, you have to keep in mind two quantities: its direction and its magnitude.
Vector (mathematics and physics)
Quantities that have only a magnitude are called scalars. If you give a scalar magnitude a direction, you create a vector. Visually, you see vectors drawn as arrows, which is perfect because an arrow has both a clear direction and a clear magnitude the length of the arrow. Take a look at the following figure.
In physics, you generally use a letter in bold type to represent a vector, although you may also see a letter with an arrow on top like this:. The arrow means that this is not only a scalar value, which would be represented by Abut also something with direction. Say that you tell some smartypants that you know all about vectors. That impresses him to no end! Take a look at this figure, which features two vectors, A and B.
They look pretty much the same — the same length and the same direction. In fact, these vectors are equal. What Is a Vector? A vector, represented by an arrow, has both a direction and a magnitude.
Equal vectors have the same length and direction but may have different starting points.Vectors are geometric representations of magnitude and direction and can be expressed as arrows in two or three dimensions.
Vectors are geometric representations of magnitude and direction which are often represented by straight arrows, starting at one point on a coordinate axis and ending at a different point.
All vectors have a length, called the magnitude, which represents some quality of interest so that the vector may be compared to another vector. Vectors, being arrows, also have a direction. This differentiates them from scalars, which are mere numbers without a direction.
A vector is defined by its magnitude and its orientation with respect to a set of coordinates. It is often useful in analyzing vectors to break them into their component parts. For two-dimensional vectors, these components are horizontal and vertical. To visualize the process of decomposing a vector into its components, begin by drawing the vector from the origin of a set of coordinates. Next, draw a straight line from the origin along the x-axis until the line is even with the tip of the original vector.
This is the horizontal component of the vector. To find the vertical component, draw a line straight up from the end of the horizontal vector until you reach the tip of the original vector. You should find you have a right triangle such that the original vector is the hypotenuse. Decomposing a vector into horizontal and vertical components is a very useful technique in understanding physics problems.
Whenever you see motion at an angle, you should think of it as moving horizontally and vertically at the same time. Simplifying vectors in this way can speed calculations and help to keep track of the motion of objects. Scalars and Vectors : Mr. Andersen explains the differences between scalar and vectors quantities.
He also uses a demonstration to show the importance of vectors and vector addition.
Components of a Vector : The original vector, defined relative to a set of axes. The horizontal component stretches from the start of the vector to its furthest x-coordinate. The vertical component stretches from the x-axis to the most vertical point on the vector.
Together, the two components and the vector form a right triangle. Scalars are physical quantities represented by a single number, and vectors are represented by both a number and a direction. Physical quantities can usually be placed into two categories, vectors and scalars. These two categories are typified by what information they require. Vectors require two pieces of information: the magnitude and direction.
In contrast, scalars require only the magnitude. Scalars can be thought of as numbers, whereas vectors must be thought of more like arrows pointing in a specific direction. A Vector : An example of a vector. Vectors are usually represented by arrows with their length representing the magnitude and their direction represented by the direction the arrow points.
Vectors require both a magnitude and a direction. The magnitude of a vector is a number for comparing one vector to another. In the geometric interpretation of a vector the vector is represented by an arrow. The arrow has two parts that define it. The two parts are its length which represents the magnitude and its direction with respect to some set of coordinate axes.
The greater the magnitude, the longer the arrow. Physical concepts such as displacement, velocity, and acceleration are all examples of quantities that can be represented by vectors.In mathematics and physicsa vector is an element of a vector space. For many specific vector spaces, the vectors have received specific names, which are listed below.
Historically, vectors were introduced in geometry and physics typically in mechanics before the formalization of the concept of vector space. Therefore, one talks often of vectors without specifying the vector space to which they belong.
Specifically, in a Euclidean spaceone considers spatial vectorsalso called Euclidean vectors which are used to represent quantities that have both magnitude and direction, and may be added and scaled that is multiplied by a real number for forming a vector space.
In classical Euclidean geometry that is in synthetic geometryvectors were introduced during 19th century as equivalence classesunder equipollenceof ordered pairs of points; two pairs AB and CD being equipollent if the points ABDCin this order, form a parallelogram.
Such an equivalence class is called a vectormore precisely, a Euclidean vector. A Euclidean vectoris thus an entity endowed with a magnitude the length of the line segment AB and a direction the direction from A to B. In physics, Euclidean vectors are used to represent physical quantities that have both magnitude and direction, but are not located at a specific place, in contrast to scalarswhich have no direction. For example, velocityforces and acceleration are represented by vectors.
In modern geometry, Euclidean spaces are often defined from linear algebra. It has been proven that the two definitions of Euclidean spaces are equivalent, and that the equivalence classes under equipollence may be identified with translations. Sometimes, Euclidean vectors are considered without reference to a Euclidean space. This makes sense, as the addition in such a vector space acts freely and transitively on the vector space itself.
This is motivated by the fact that every Euclidean space of dimension n is isomorphic to the Euclidean space R n. By Gram—Schmidt processone may also find an orthonormal basis of the associated vector space a basis such that the inner product of two basis vectors is 0 if they are different and 1 if they are equal.
When such tuples are used for representing some data, it is common to call them vectors even if the vector addition does not mean anything for these data, which may make the terminology confusing. Similarly, some physical phenomena involve a direction and a magnitude.
They are often represented by vectors, even if operations of vector spaces do not apply to them. Every algebra over a field is a vector space, but elements of an algebra are generally not called vectors. However, in some cases, they are called vectorsmainly for historical reasons. A vector field is a vector-valued function that, generally, has a domain of the same dimension as a manifold as its codomain. From Wikipedia, the free encyclopedia.
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