Question

A certain vector is given by $\overrightarrow{OP}=3\hat{i}+4\hat{j}+7\hat{k}$. The angle made by it with Z-axis is:

• A. $co{s}^{-1}(\frac{3}{94})$
• B. $co{s}^{-1}(\frac{4}{74})$
• C. $co{s}^{-1}(\frac{7}{74})$
• D. $co{s}^{-1}(\frac{7}{\sqrt{74}})$

Answer 1

The correct option is D $co{s}^{-1}(\frac{7}{\sqrt{74}})$

$\overrightarrow{OP}=3\hat{i}+4\hat{j}+7\hat{k}$

Unit vector along z axis is $\hat{k}$.

The angle between z axis and $\overrightarrow{OP}$ is given as: $\cos \theta =\frac{\overrightarrow{OP}.\hat{k}}{|\overrightarrow{OP}|}$

$\cos \theta =\frac{(3\hat{i}+4\hat{j}+7\hat{k}).\hat{k}}{\sqrt{3^2+4^2+7^2}}$

$\cos \theta =\frac{7}{\sqrt{74}}$

$\theta ={\cos }^{-1}\frac{7}{\sqrt{74}}$