Question

30 unit If the value of an angle with the x-axis of a vector is 70 °, the value of the angle with the y axis is 60, what is the value of the angle with the z-axis?

Answer 1

Answer: $37.28^{\circ}$

Explanation:

Given

Angle made with the x-axis is $\alpha=70^{\circ}$

Angle made with the y-axis is $\beta=60^{\circ}$

Suppose angle made with z-axis is $\gamma$

$\therefore \cos^2\alpha+\cos^2\beta+\cos^2\gamma =1$

Inserting values

$\Rightarrow \cos^2(70^{\circ})+\cos^2(60^{\circ})+\cos^2\gamma=1\\\Rightarrow 0.1169+0.25+\cos^2\gamma=1\\\Rightarrow \cos^2\gamma=0.6331\\\Rightarrow \cos \gamma=0.7956\\\Rightarrow \gamma=37.28^{\circ}$