The Handy Math Answer Book

points in the plane with xand
ycoordinates whose respec-
tive differences are 3 and 4. All
these vectors are parallel to
each other, equal, and have
the same magnitude and
direction. Therefore, any vec-
tor with components of aand
bcan be said to be equal to the
vector [a, b].

How is the magnitude of a

vectordetermined?

The magnitude of a vector is
equivalent to the length of a
vector. Placing a pair of verti-
cal lines (similar to the
absolute value symbol) around
a vector implies the magni-
tude of the vector. For exam-
ple, if the variable V is used to
represent a vector, then the
expression |V| indicates the
magnitude of the vector.

What do columns and

rowsmean when discussing vectors?

Vectors can be described by columns and rows. For example, two-dimensional and
three-dimensional vectors are usually represented as a single vertical column of
numeric values. The following lists such columns in two and three dimensions:

A two-dimensional vector illustrated with columns and rows would look like this:

And a three-dimensional vector would look like this using columns and rows:

x

y

z

V=

Vy

x

=

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MATHEMATICAL ANALYSIS

Vectors are used to indicate displacement between two points in

space, such as, for example, the distance and direction travelled by

a rocket from its launch point to its present position. Reportage/

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