7.5: Scalar and Vector Projections
We are going to use the dot product with the concept of
projection.
Projection: is putting one thing on another (defined by Me :) )
When two vectors a = OA and b = OB are placed tail to tail, and 0
is the angle between them, the scalar projection of a on b is ON.
To solve for the scalar projection of a on b:
from the dot product we know: a b = |a||b|cos 0
May 23­8:38 AM
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Example 1:
For the vectors a = (­3, 4, 5 3) and b = (­2, 2, ­1), calculate each of the following scalar projections:
a) a on b
b) b on a
May 22­8:45 PM
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Example 2:
Determine the angle that the vector OP = (2, 1, 4) makes with each of the coordinate axis. May 23­8:45 AM
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Example 3:
Find the vector projection of OA = (4,3) on OB = (4, ­1).
Homework
p. 398­399 #5, 6, 7, 8a, 11, 14 May 22­8:53 PM
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May 23­1:27 PM
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