AP Physics C - Quiz 1 Vectors

anticommutative property

change in the order of operation introduces the minus sign

antiparallel vectors

two vectors with directions that differ by 180°

associative

terms can be grouped in any fashion

commutative

operations can be performed in any order

component form of a vector

a vector written as the vector sum of its components in terms of unit vectors

corkscrew right-hand rule

a rule used to determine the direction of the vector product

cross product

the result of the vector multiplication of vectors is a vector called a cross product; also called a vector product

difference of two vectors

vector sum of the first vector with the vector antiparallel to the second

direction angle

in a plane, an angle between the positive direction of the x-axis and the vector, measured
counterclockwise from the axis to the vector

displacement

change in position

distributive

multiplication can be distributed over terms in summation

dot product

the result of the scalar multiplication of two vectors is a scalar called a dot product; also called a scalar product

equal vectors

two vectors are equal if and only if all their corresponding components are equal; alternately, two parallel vectors of equal magnitudes

magnitude

length of a vector

null vector

a vector with all its components equal to zero

orthogonal vectors

two vectors with directions that differ by exactly 90° , synonymous with perpendicular vectors

parallel vectors

two vectors with exactly the same direction angles

parallelogram rule

geometric construction of the vector sum in a plane

polar coordinate system

an orthogonal coordinate system where location in a plane is given by polar coordinates

polar coordinates

a radial coordinate and an angle

radial coordinate

distance to the origin in a polar coordinate system

resultant vector

vector sum of two (or more) vectors

scalar

a number, synonymous with a scalar quantity in physics

scalar component

a number that multiplies a unit vector in a vector component of a vector

scalar equation

equation in which the left-hand and right-hand sides are numbers

scalar product

the result of the scalar multiplication of two vectors is a scalar called a scalar product; also called a dot product

scalar quantity

quantity that can be specified completely by a single number with an appropriate physical unit

tail-to-head geometric construction

geometric construction for drawing the resultant vector of many vectors

unit vector

vector of a unit magnitude that specifies direction; has no physical unit

unit vectors of the axes

unit vectors that define orthogonal directions in a plane or in space

vector

mathematical object with magnitude and direction

vector components

orthogonal components of a vector; a vector is the vector sum of its vector components.

vector equation

equation in which the left-hand and right-hand sides are vectors

vector product

the result of the vector multiplication of vectors is a vector called a vector product; also called a cross product

vector quantity

physical quantity described by a mathematical vector—that is, by specifying both its magnitude and its direction; synonymous with a vector in physics

vector sum

resultant of the combination of two (or more) vectors

scalar, positive, negative

When a vector is multiplied by a __________, the result is another vector of a different length than the length of the original
vector. Multiplication by a __________ scalar does not change the original direction; only the magnitude is affected.
Multiplication by a __________ scalar reverses the original direction. The resulting vector is antiparallel to the original
vector. Multiplication by a scalar is distributive. Vectors can be divided by nonzero scalars but cannot be divided by vectors.

x, y

In a plane, there are two equivalent coordinate systems. The Cartesian coordinate system is defined by unit vectors
i^ and j^ along the __________-axis and the __________-axis, respectively. The polar coordinate system is defined by the radial unitvector r^, which gives the direction from the origin, and a unit vector t^, which is perpendicular (orthogonal) to
the radial direction.

perpendicular

The vector product of two vectors is a vector __________ to both of them.