Question

If a vector à makes angles 45° and 60°
with x and y axis respectively then angle
made by it with z-axis.​

Answer 1

If a vector à makes angles 45° and 60° with x and y axes respectively then angle made. by it with z-axis is 30 degrees.

Answer 2

Answer:

The angle made by vector A with z-axis will be 60°.

Step by step explanation:

• Consider that, the vector A makes an angle α, β and γ with x-axis, y-axis and z-axis respectively.
• It is given that, α = 45° and β =60°.
• To find the angle γ, we can use condition:

                $cos^{2}\alpha +cos^{2}\beta +cos^{2}\gamma=1$

              $cos^{2}45+cos^{2} 60+cos^{2}\gamma=1$

                  $(\frac{1}{\sqrt{2}})^2 + (\frac{1}{2})^2 + cos^{2}\gamma =1$

                             $\frac{1}{2} +\frac{1}{4} + cos^{2}\gamma=1$

                                        $cos^{2}\gamma=1-\frac{3}{4}$

                                         $cos^{2}\gamma=\frac{1}{4}$

                                         $cos\gamma=\frac{1}{2} }$

             ∴                               γ = 60°

         Therefore, the vector A makes angle of 60° with z-axis.