   Chapter 12.3, Problem 36E

Chapter
Section
Textbook Problem

# Find the direction cosines and direction angles of the vector. (Give the direction angles correct to the nearest degree.)36. 1 2 i + j + k

To determine

To find: The direction cosines of the vector and the direction angles of the vector.

Explanation

Given:

12i+j+k (1)

Formula:

Consider three dimensional vector a as follows.

a=a1i+a2j+a3k (2)

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

|a|=a12+a22+a32 (3)

Direction cosines are,

cosα=a1|a| (4)

cosβ=a2|a| (5)

cosγ=a3|a| (6)

Compare equations (1) and (2).

a=12,1,1 .

In equation (3), substitute 12 for a1 , 1 for a2 and 1 for a3 .

|a|=(12)2+(1)2+(1)2=14+1+1=94=32

In equation (4), substitute 32 for |a| and 12 for a1 .

cosα=(12)(32)=13

In equation (5), substitute 32 for |a| and 1 for a2 .

cosβ=1(32)=23

In equation (6), substitute 32 for |a| and 1 for a3

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