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?
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: [tex]37.28^{\circ}[/tex]
Explanation:
Given
Angle made with the x-axis is [tex]\alpha=70^{\circ}[/tex]
Angle made with the y-axis is [tex]\beta=60^{\circ}[/tex]
Suppose angle made with z-axis is [tex]\gamma[/tex]
[tex]\therefore \cos^2\alpha+\cos^2\beta+\cos^2\gamma =1[/tex]
Inserting values
[tex]\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}[/tex]