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)`

Step-by-step 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)`