   Chapter 11.3, Problem 31E

Chapter
Section
Textbook Problem

# Finding Direction Angles In Exercises 29-34, find the direction cosines and angles of u, and demonstrate that the sum of the squares of the direction cosines is 1.u = 3i + 2j – 2k

To determine

To calculate: The direction cosines and angles of u=3i+2j2k and show that the sum of squares of direction cosines is equal to 1.

Explanation

Given:

The vector-valued function is: u=3i+2j2k.

Formula used:

If v=v1,v2,v3. Then, the direction cosines are:

cosα=v1vcosβ=v2vcosγ=v3v

Calculation:

Consider the provided vector,

u=3i+2j2k

Then,

u=32+22+22=9+4+4=17

Then, the direction cosines will be:

cosα=317

And the corresponding angle is,

α=arccos(317)43.3°

Also,

cosβ=217

And the corresponding angle is,

β=arccos(23)61.0°

And,

cosγ=217

And the corresponding angle is,

γ=arccos(23)=119

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