$ABC$ is a triangle in a plane with vertices $A(2, 3, 5)$,$B(-1, 3, 2)$,and $C(\lambda, 5, \mu)$. If the median through $A$ is equally inclined to the coordinate axes,then the value of $(\lambda^3 + \mu^3 + 5)$ is

Find the direction cosines and the length of a vector whose projections on the coordinate axes are $6, -3, 2$.

Let $O$ be the origin and $P$ be a point which is at a distance of $3$ units from the origin. If the direction ratios of $\vec{OP}$ are $(1, -2, -2)$,then the coordinates of $P$ are

Which of the following statements is false?

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?

If the direction cosines of two lines are given by $l+m+n=0$ and $l^2-5m^2+n^2=0$, then the angle between them is