If the vectors $6i - 2j + 3k$,$2i + 3j - 6k$,and $3i + 6j - 2k$ are the position vectors of the vertices of a triangle,then the triangle is

The position vectors of the vertices of $\triangle ABC$ are $4\hat{i} - 2\hat{j}$,$\hat{i} + 4\hat{j} - 3\hat{k}$,and $-\hat{i} + 5\hat{j} + \hat{k}$ respectively. Then,$m \angle ABC = $

If a particle is acted upon by forces of magnitude $6$ and $7$ units in the directions of $-\hat{i} - 2\hat{j} + 2\hat{k}$ and $2\hat{i} - 3\hat{j} - 6\hat{k}$ respectively,and it undergoes a displacement from point $P(2, -1, -3)$ to $Q(5, -1, 1)$,then the work done by the forces is .......... units.

If $a=\hat{i}+\hat{j}+t \hat{k}$ and $b=\hat{i}+2 \hat{j}+3 \hat{k}$,then the values of $t$ for which $(a+b)$ and $(a-b)$ are perpendicular are:

If $P(6, 10, 10)$,$Q(1, 0, -5)$,$R(6, -10, \lambda)$ are vertices of a triangle right-angled at $Q$,then the value of $\lambda$ is ....

The component of $\hat{i}$ in the direction of the vector $\hat{i}+\hat{j}+2 \hat{k}$ is