vector

(noun)

A directed quantity, one with both magnitude and direction; the between two points.

Related Terms

Examples of vector in the following topics:

  • Components of a Vector

    • 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.
    • To visualize the process of decomposing a vector into its components, begin by drawing the vector from the origin of a set of coordinates.
    • This is the horizontal component of the vector.
    • He also uses a demonstration to show the importance of vectors and vector addition.

  • Adding and Subtracting Vectors Graphically

    • Draw a new vector from the origin to the head of the last vector.
    • Since vectors are graphical visualizations, addition and subtraction of vectors can be done graphically.
    • This new line is the vector result of adding those vectors together.
    • Then, to subtract a vector, proceed as if adding the opposite of that vector.
    • Draw a new vector from the origin to the head of the last vector.

  • Multiplying Vectors by a Scalar

    • Multiplying a vector by a scalar changes the magnitude of the vector but not the direction.
    • A scalar, however, cannot be multiplied by a vector.
    • To multiply a vector by a scalar, simply multiply the similar components, that is, the vector's magnitude by the scalar's magnitude.
    • Most of the units used in vector quantities are intrinsically scalars multiplied by the vector.
    • (i) Multiplying the vector $A$ by the scalar $a=0.5$ yields the vector $B$ which is half as long.

  • Unit Vectors and Multiplication by a Scalar

    • In addition to adding vectors, vectors can also be multiplied by constants known as scalars.
    • When multiplying a vector by a scalar, the direction of the vector is unchanged and the magnitude is multiplied by the magnitude of the scalar .
    • Once you have the vector's components, multiply each of the components by the scalar to get the new components and thus the new vector.
    • A useful concept in the study of vectors and geometry is the concept of a unit vector.
    • A unit vector is a vector with a length or magnitude of one.

  • Adding and Subtracting Vectors Using Components

    • Another way of adding vectors is to add the components.
    • If we were to add this to another vector of the same magnitude and direction, we would get a vector twice as long at the same angle.
    • This new line is the resultant vector.
    • Vector Addition Lesson 2 of 2: How to Add Vectors by Components
    • This video gets viewers started with vector addition using a mathematical approach and shows vector addition by components.

  • Scalars vs. Vectors

    • 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.
    • Scalars differ from vectors in that they do not have a direction.
    • An example of a vector.

  • Introduction to Scalars and Vectors

    • Given this information, is speed a scalar or a vector quantity?
    • Displacement is an example of a vector quantity.
    • In mathematics, physics, and engineering, a vector is a geometric object that has a magnitude (or length) and direction and can be added to other vectors according to vector algebra.
    • (A comparison of scalars vs. vectors is shown in . )
    • He also uses a demonstration to show the importance of vectors and vector addition.

  • Linear Vector Spaces

    • We can add any two, say, force vectors and get another force vector.
    • We can also scale any such vector by a numerical quantity and still have a legitimate vector.
    • Whereas our use of vector spaces is purely abstract.
    • The simplest example of a vector space is $\mathbf{R}^n$ , whose vectors are n-tuples of real numbers.
    • So trivially, $F$ is a vector space over $F$ .

  • Position, Displacement, Velocity, and Acceleration as Vectors

    • Figure 1 shows an example of how to use a vector to visually represent an object in physics.
    • Vectors can be used to represent physical quantities.
    • Vectors are a combination of magnitude and direction, and are drawn as arrows.
    • Because vectors are constructed this way, it is helpful to analyze physical quantities (with both size and direction) as vectors.
    • In drawing the vector, the magnitude is only important as a way to compare two vectors of the same units.

  • Superposition of Fields

    • As vector fields, electric fields obey the superposition principle.
    • Possible stimuli include but are not limited to: numbers, functions, vectors, vector fields, and time-varying signals.
    • Vector addition is commutative, so whether adding A to B or B to A makes no difference on the resultant vector; this is also the case for subtraction of vectors.
    • To do this, first find the component vectors of force applied by each field in each of the orthogonal axes.
    • Their sum is commutative, and results in a resultant vector c.