Let $(\bar{p} \wedge \bar{q})$ denote the angle between $\bar{p}$ and $\bar{q}$. If $\bar{a} + \bar{b} + \bar{c} = \bar{0}, |\bar{a}| = 7, |\bar{b}| = 5$ and $|\bar{c}| = 3$ then (take $\pi = \dfrac{22}{7}$)

If the lines $\dfrac{x-5}{5m+2} = \dfrac{2-y}{5} = \dfrac{1-z}{-1}$ and $x = \dfrac{2y+1}{4m} = \dfrac{1-z}{-3}$ are perpendicular to each other, then the value of m is ...

For the line $\dfrac{x+1}{1} = \dfrac{y-2}{2} = \dfrac{z+3}{3}$, identify the incorrect statement among the following.

The direction cosines of a line which is perpendicular to the lines $\dfrac{x-7}{2} = \dfrac{y+17}{-3} = \dfrac{z-6}{1}$ and $\dfrac{x+5}{1} = \dfrac{y+3}{2} = \dfrac{z-6}{-2}$ are...