Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 12 - Vectors and the Geometry of Space - Review - Concept Check - Page 881: 7

Answer

Scalar projection of $b$ onto $a$ is defined as: $comp_ab=\dfrac{a \cdot b}{|a|}$ Vector projection of $b$ onto $a$ is defined as: $proj_ab$=Scalar projection $\times$ unit vector in direction $a$ $=\dfrac{a \cdot b}{|a|} \times \frac{a}{|a|}$ $=\dfrac{a \cdot b}{|a|^2} a$ See the attached graph.

Work Step by Step

Scalar projection of $b$ onto $a$ is defined as: $comp_ab=\dfrac{a \cdot b}{|a|}$ Vector projection of $b$ onto $a$ is defined as: $proj_ab$=Scalar projection $\times$ unit vector in direction $a$ $=\dfrac{a \cdot b}{|a|} \times \frac{a}{|a|}$ $=\dfrac{a \cdot b}{|a|^2} a$ See the attached graph.
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