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As a check, the reader may wish to verify that the vectors and a are perpendicular by showing that their dot product
is zero.
A formula for the length of the vector component of u along a can be obtained by writing
which yields
If.θ denotes the angle between u and a, then , so 10 can also be written as (10)
(11)
(Verify.) A geometric interpretation of this result is given in Figure 3.3.7.
Figure 3.3.7
As an example, we will use vector methods to derive a formula for the distance from a point in the plane to a line.
EXAMPLE 7 Distance Between a Point and a Line
Find a formula for the distance D between point and the line .
Solution
