The components of a vector $a$ along and perpendicular to the non-zero vector $b$ are respectively:

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:

Assertion $(A)$: $a, b, c, d$ are position vectors of $4$ points such that $2a - 3b + 7c - 6d = 0 \Rightarrow a, b, c, d$ are coplanar.
Reason $(R)$: Vector equation of the plane passing through three points whose position vectors are $a, b, c$ is $r = (1 - x - y)a + xb + yc$.
Which of the following is true?

Find the angle between the vectors $2 \hat{i}-\hat{j}+\hat{k}$ and $3 \hat{i}+4 \hat{j}-\hat{k}$.

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.