Let $\vec{a}=\hat{i}+2 \hat{j}+4 \hat{k}, \vec{b}=\hat{i}+\lambda \hat{j}+4 \hat{k}$ and $\overrightarrow{\mathrm{c}}=2 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+\left(\lambda^2-1\right) \hat{\mathrm{k}}$ be coplanar vectors. Then the non-zero vector $\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{c}}$ is :

The plane containing the line $\frac{x-3}{2}=\frac{y+2}{-1}=\frac{z-1}{3}$ and also containing its projection on the plane $2 x+3 y-z=$ 5 , contains which one of the following...

The distance of the point having position vector $-\hat{i}+2 \hat{j}+6 \hat{k}$ from the straight line passing through the point ( $2,3,-4$ ) and parallel to...