Question

Find the projection of the vector
A=i−2j+k
on the vector
B=4i−4j+7K

1/5

4/7

19/9

11/5

Answer 1

Answer on Question #56013 – Math – Vector Calculus

Find the projection of the vector

A=i-2j+k

on the vector

B=4i-4j+7K

1/5

4/7

19/9

11/5

Solution

The projection of the vector $\vec{A}$ on the vector $\vec{B}$ is

$$\frac {\vec {A} \cdot \vec {B}}{| \vec {B} |} = \frac {1 \cdot 4 + (- 2) \cdot (- 4) + 1 \cdot 7}{\sqrt {4 ^ {2} + (- 4) ^ {2} + 7 ^ {2}}} = \frac {1 9}{\sqrt {8 1}} = \frac {1 9}{9}.$$

Answer: 19/9.

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