$A$ particle acted on by constant forces $4i + j - 3k$ and $3i + j - k$ is displaced from the point $i + 2j + 3k$ to the point $5i + 4j + k$. The total work done by the force is ............... $unit$.

The orthogonal projection vector of $\vec{a} = 2\hat{i} + 3\hat{j} + 3\hat{k}$ on $\vec{b} = \hat{i} - 2\hat{j} + \hat{k}$ is

The angle between two diagonals of a cube is:

Let the points $A, B$ and $P$ be $(-2, 2, 4), (2, 6, 3)$ and $(1, 2, 1)$ respectively. The magnitude of the moment of the force represented by $\overrightarrow{AB}$ and acting at $A$ about $P$ is

Let $\overline{a}, \overline{b}$,and $\overline{c}$ be three non-zero vectors such that no two of these are collinear. If the vector $\overline{a}+2\overline{b}$ is collinear with $\overline{c}$ and $\overline{b}+3\overline{c}$ is collinear with $\overline{a}$,then $\overline{a}+2\overline{b}+6\overline{c}$ equals

If $\vec{l}, \vec{m}, \vec{n}$ are coplanar vectors,for what value of $\lambda$ are the points with position vectors $\vec{l} - 2\vec{m} + 3\vec{n}$,$2\vec{l} + \lambda\vec{m} - 4\vec{n}$,and $-7\vec{m} + 10\vec{n}$ collinear?