Question

The angles which the vector $\overrightarrow{A}=3\hat{i}+6\hat{j}+2\hat{k}$ makes with the co-ordinate axes are:

• A. $co{s}^{-1}\frac{3}{7},co{s}^{-1}\frac{4}{7},co{s}^{-1}\frac{1}{7}$
• B. $co{s}^{-1}\frac{3}{7},co{s}^{-1}\frac{6}{7},co{s}^{-1}\frac{2}{7}$
• C. $co{s}^{-1}\frac{4}{7},co{s}^{-1}\frac{5}{7},co{s}^{-1}\frac{3}{7}$
• D. None of these

Answer 1

The correct option is B $co{s}^{-1}\frac{3}{7},co{s}^{-1}\frac{6}{7},co{s}^{-1}\frac{2}{7}$

$\hat{A}=\frac{3\hat{i}+6\hat{j}+2\hat{k}}{\sqrt{9+36+4}}=(\frac{3}{7}\hat{i}+\frac{6}{7}\hat{j}+\frac{2}{7}\hat{k})$
If $\alpha ,\beta and\gamma$ are angles made by $\overrightarrow{A}$ with coordinates axes, the $cos\alpha =\frac{3}{7},cos\beta =\frac{6}{7}andcos\gamma =\frac{2}{7}$