   Chapter 11.3, Problem 29E

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 = i + 2 j + 2 k

To determine

To calculate: The direction cosines and angles of the vector u=i+2j+2k and show that,

cos2α+cos2β+cos2γ=1.

Explanation

Given:

The vector-valued function is u=i+2j+2k.

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=i+2j+2k

Then,

u=12+22+22=3

Then, the direction cosines will be:

cosα=13α=arccos(13)α70.5°

Also,

cosβ=23β=arccos(23)β48

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Simplify the expressions in Exercises 97106. x1/2yx2y3/2

Finite Mathematics and Applied Calculus (MindTap Course List)

#### Evaluate tanxdx.

Calculus: Early Transcendentals

#### Find a formula for the inverse of the function. 24. y=x2x,x12

Single Variable Calculus: Early Transcendentals, Volume I

#### True or False: y′ + xey = ex+y is separable.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 