List of top Mathematics Questions on Coplanarity of Two Lines asked in KEAM

If \( |\mathbf{a} - \mathbf{b}| = \frac{\sqrt{3}}{2} \) where \( \mathbf{a} \) and \( \mathbf{b} \) are unit vectors, find the angle between \( \mathbf{a} \) and \( \mathbf{b} \).

If the lines $\dfrac{x-4}{m} = \dfrac{y-3}{2} = \dfrac{z+2}{1}$ and $\dfrac{x-3}{1} = \dfrac{y-4}{1} = \dfrac{z+3}{m}$ are coplanar, then the values of $m$ are

If the lines \( \frac{x+3}{-3} = \frac{y-1}{k} = \frac{z-5}{5} \) and \( \frac{x+1}{-1} = \frac{y-2}{2} = \frac{z-5}{5} \) are coplanar, then the value of \( k \) is

The perpendicular distance from the point $(1, -1)$ to the line $x + 5y - 9 = 0$ is equal to