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# help

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A vector makes an angle of 30 degrees with the x-axis, and an angle of 80 degrees with the y-axis.  Find the angle between the vector and the z-axis.

Dec 13, 2019

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A vector makes an angle of 30 degrees with the x-axis, and an angle of 80 degrees with the y-axis.

Find the angle between the vector and the z-axis.

Formula: $$\boxed{ \cos{\alpha_x}+\cos{\alpha_y}+\cos{\alpha_z} = 1 }$$

$$\begin{array}{|rcll|} \hline \mathbf{\cos{\alpha_x}+\cos{\alpha_y}+\cos{\alpha_z} } &=& \mathbf{ 1 } \quad | \quad \alpha_x = 30^\circ,\ \alpha_y = 80^\circ \\\\ \cos{30^\circ}+\cos{80^\circ}+\cos{\alpha_z} &=& 1 \\ \cos{\alpha_z} &=& 1-\cos{30^\circ}-\cos{80^\circ}\\ \cos{\alpha_z} &=& -0.03967358145\\ \mathbf{\alpha_z} &=& \mathbf{92.2737255129^\circ} \\ \hline \end{array}$$

Dec 13, 2019