   Chapter 12.3, Problem 34E

Chapter
Section
Textbook Problem

# Find the direction cosines and direction angles of the vector. (Give the direction angles correct to the nearest degree.)34. ⟨6, 3, −2⟩

To determine

To find: The direction cosines of the vector.

Explanation

Given:

6,3,2

Formula:

Consider a general expression to find magnitude of a three dimensional vector that is a=a1,a2,a3 .

|a|=a12+a22+a32 (1)

Direction cosines are,

cosα=a1|a| (2)

cosβ=a2|a| (3)

cosγ=a3|a| (4)

Consider a=6,3,2 .

In equation (1), substitute 6 for a1 , 3 for a2 and –2 for a3 .

|a|=(6)2+(3)2+(2)2=36+9+4=49=7

In equation (2), substitute 7 for |a| and 6 for a1 .

cosα=67

In equation (3), substitute 7 for |a| and 3 for a2 .

cosβ=37

In equation (4), substitute 7 for |a| and –2 for a3 .

cosγ=27

Thus, the direction cosines of the vector are cosα=67_ , cosβ=37_ and cosγ=27_

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