157
Summary
Selected Vocabulary
vector................................a quantity that has both an amount (magnitude) and a direction in space
magnitude.........................the “amount” associated with a vector
scalar.................................a quantity that has no direction in space, only an amount
Notation
A.......................................vector with components A
x
, A
y
, and A
z
A
......................................handwritten notation for a vector
|A|.....................................the magnitude of vector A
r........................................the vector whose components are x, y, and z
.
r......................................the vector whose components are
.
x,
.
y, and
.
z
x
,y
,z
...............................
(optional topic) unit vectors; the vectors with magnitude 1 lying along the
x, y, and z axes
i
,j
,k
...............................
a harder to remember notation for the unit vectors
Standard Terminology Avoided in This Book
displacement vector...........a name for the symbol
.
r
speed.................................the magnitude of the velocity vector, i.e. the velocity stripped of any
information about its direction
Summary
A vector is a quantity that has both a magnitude (amount) and a direction in space, as opposed to a scalar,
which has no direction. The vector notation amounts simply to an abbreviation for writing the vector’s three
components.
In two dimensions, a vector can be represented either by its two components or by its magnitude and
direction. The two ways of describing a vector can be related by trigonometry.
The two main operations on vectors are addition of a vector to a vector, and multiplication of a vector by a
scalar.
Vector addition means adding the components of two vectors to form the components of a new vector. In
graphical terms, this corresponds to drawing the vectors as two arrows laid tip-to-tail and drawing the sum
vector from the tail of the first vector to the tip of the second one. Vector subtraction is performed by negating
the vector to be subtracted and then adding.
Multiplying a vector by a scalar means multiplying each of its components by the scalar to create a new
vector. Division by a scalar is defined similarly.
Summary