   Chapter 11.3, Problem 33E

Chapter
Section
Textbook Problem

# Finding Direction AnglesIn Exercises 31–36, find the direction cosines and angles of u and show that cos 2 α + cos 2 β + cos 2 γ = 1 . u = 〈 0 , 6 , − 4 〉

To determine

To calculate: The direction cosines and angles of the vector u=0,6,4 and show that,

cos2α+cos2β+cos2γ=1.

Explanation

Given:

The vector-valued function is u=0,6,4.

Formula used:

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

cosα=v1vcosβ=v2vcosγ=v3v

Calculation:

Consider the vector,

u=0,6,4

Then, the magnitude of the vector u is;

u=0+62+(4)2=36+16=213

Then, the direction cosines will be:

cosα=0213cosα=0α=90°

Also,

cosβ=6213cosβ=0

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