If the sum of the distances of the point $P(3, 4, \alpha)$,where $\alpha \in R$,from the $X$-axis,$Y$-axis,and $Z$-axis is minimum,then $\sec \alpha =$

Let $\alpha$ be the angle between the lines whose direction cosines satisfy the equations $l+m-n=0$ and $l^{2}+m^{2}-n^{2}=0$. Then the value of $\sin^{4} \alpha + \cos^{4} \alpha$ 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 line segment joining the points $(2,1,-3)$ and $(-1,0,2)$ on the line whose direction ratios are $3,2,6$ is

If the direction cosines of a line are $\left(\frac{a}{\sqrt{83}}, \frac{5}{\sqrt{83}}, \frac{c}{\sqrt{83}}\right)$ and $c-a=4$,then $ca=$

If a line makes angles of $120^{\circ}$ and $60^{\circ}$ with the $x$ and $y$ axes respectively,what angle does it make with the $z$ axis?