If $\alpha, \beta, \gamma$ are the angles made by a line with $x, y,$ and $z$ axes respectively such that $2\left( \frac{\tan^2 \alpha}{1 + \tan^2 \alpha} + \frac{\tan^2 \beta}{1 + \tan^2 \beta} + \frac{\tan^2 \gamma}{1 + \tan^2 \gamma} \right) = 3 \sec^2 \frac{\theta}{2}$,then $\theta =$

The angle between the lines whose direction ratios satisfy the equations $l+m+n=0$ and $l^2=m^2+n^2$ is

The acute angle between the lines whose direction cosines are given by the equations $l+m+n=0$ and $2lm+2ln-mn=0$ is

Consider the following statements:
Assertion $(A)$: The direction ratios of a line $L_1$ are $2, 5, 7$ and the direction ratios of another line $L_2$ are $\frac{4}{\sqrt{19}}, \frac{10}{\sqrt{19}}, \frac{14}{\sqrt{19}}$. Then the lines $L_1, L_2$ are parallel.
Reason $(R)$: If the direction ratios of a line $L_1$ are $a_1, b_1, c_1$,the direction ratios of a line $L_2$ are $a_2, b_2, c_2$ and $a_1 a_2 + b_1 b_2 + c_1 c_2 = 0$,then the lines $L_1, L_2$ are parallel. Which one of the following is true?

The projection of the point $(a, b, c)$ on the $yz$-plane is:

Find a vector $\vec{r}$ of magnitude $3 \sqrt{2}$ units which makes an angle of $\frac{\pi}{4}$ and $\frac{\pi}{2}$ with $y$ and $z$-axes,respectively.