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Question: The direction cosines of ![](https://cdn.pureessence.tech/canvas_637.png?top_left_x=1343&top_left_y=...

The direction cosines of are

A

1, 1, 1

B

2, 2, 2

C

12,12,12\frac { 1 } { \sqrt { 2 } } , \frac { 1 } { \sqrt { 2 } } , \frac { 1 } { \sqrt { 2 } }

D

13,13,13\frac { 1 } { \sqrt { 3 } } , \frac { 1 } { \sqrt { 3 } } , \frac { 1 } { \sqrt { 3 } }

Answer

13,13,13\frac { 1 } { \sqrt { 3 } } , \frac { 1 } { \sqrt { 3 } } , \frac { 1 } { \sqrt { 3 } }

Explanation

Solution

Let

∴\therefore

And

A=Ax2+Ay2+Az2=(1)2+(1)2+(1)2=3A = \sqrt { A _ { x } ^ { 2 } + A _ { y } ^ { 2 } + A _ { z } ^ { 2 } } = \sqrt { ( 1 ) ^ { 2 } + ( 1 ) ^ { 2 } + ( 1 ) ^ { 2 } } = \sqrt { 3 }

Cos β\betaand cosγ\gammaare the directions cosines of .

∴cos⁡α=AxA=13\therefore \cos \alpha = \frac { \mathrm { A } _ { \mathrm { x } } } { \mathrm { A } } = \frac { 1 } { \sqrt { 3 } }