   Chapter 11.3, Problem 41E

Chapter
Section
Textbook Problem

# Finding the Projection of u onto v In Exercises 37—-44, (a) find the projection of u onto v and (b) find the vector component of u orthogonal to v. u = − 9 i − 2 j − 4 k,   v = 4 j + 4 k

(a)

To determine

To calculate: The coordinate of projection of vector u=9i2j4k onto v=4j+4k.

Explanation

Given:

The vectors are u=9i2j4k and v=4j+4k.

Formula used:

The projection of vector v onto the vector u is given by projvu=(uvv2)v.

Calculation:

If u and v are non-zero vectors, then, the projection of u onto v is given by,

projvu=(uvv2)v.

Let

w1=projvu=(uvv2)

Here,

u=9i2j

(b)

To determine

To calculate: The coordinate of the vector component of u=9i2j4k orthogonal to v=4j+4k.

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