MAT 21C Lecture Notes - Lecture 13: Global Positioning System, Unit Vector, Dot Product
MAT 21C – Lecture 13 – Vectors and the Dot Product
• A vector is a quantity with magnitude and direction.
• Analytically, vectors are represented by components:
in 2
dimensions and
in 3 dimensions.
• Example: Given , then
.
• Given vector
, the magnitude of the vector is
. The distance between P and Q is
.
• Vector Algebra: Given vectors and
and ,
then
.
For any constant k, then
.
.
• The vector
is a unit vector if
In 3 dimensions, the standard unit
vectors are:
.
• There are two ways to write a vector,
which are: 1)
OR 2)
. The direction of
is
• Example: Find the magnitude and direction for
The magnitude of
is
The direction of
is
• In two dimensions, the standard unit vectors are:
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MAT 21C Full Course Notes
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