Question

Find the vector projection of 5 − 4+ along the vector 3 − 2+ 4?

Answer 1

Answer:

Examples for The projection of a vector

Example 1

Given v = i - 2j + 2k and u = 4i - 3k find

the component of v in the direction of u,

the projection of v in the direction of u,

the resolution of v into components parallel and perpendicular to u

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Solution

We have u · v = -2, |v| = 3 and |u| = 5.

The component of v in the direction of u is

u-· v --2 |u| = 5 .

The projection of v in the direction of u is

u-· v --2 8-- 6-- |u |2 u = 52 (4i- 3k) = - 25i + 25k.

To calculate the resolution of v into components parallel and perpendicular to u we find the component parallel to u and that is just the projection of v in the direction of u - this we have calculated in part (b). The component perpendicular to u is