Question

Find the angle between the line of intersection of the planes $\overrightarrow{r}.(i+2j+3k)=0$ and $\overrightarrow{r}.(3i+2j+3k)=0$ with coordinate axes

• A. with $x$-axis $\frac{\pi }{2}$
• B. with $y$-axis ${\cos }^{-1}\left(\frac{3}{\sqrt{13}}\right)$
• C. with $y$-axis ${\cos }^{-1}\left(\frac{2}{\sqrt{13}}\right)$
• D. all of these

Answer 1

Answer: (A), (B)

The correct options are
A with $x$-axis $\frac{\pi }{2}$
B with $y$-axis ${\cos }^{-1}\left(\frac{3}{\sqrt{13}}\right)$

Direction ratios: $\left|\begin{array}{ccc}i& j& k\\ 1& 2& 3\\ 3& 2& 3\end{array}\right|=(0,6,4)$ or $(-,3,-2)$

Therefore angle with $x$-axis: $\frac{\pi }{2}$

with $y$- axis ${\cos }^{-1}\left(\frac{3}{\sqrt{13}}\right)$

with $z$-axis ${\cos }^{-1}\left(\frac{-2}{\sqrt{13}}\right)$