University Physics Volume 1

# Key Terms

### Key Terms

anticommutative property
change in the order of operation introduces the minus sign
antiparallel vectors
two vectors with directions that differ by $180°180°$
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 $90°90°$, 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
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
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