If the vectors $3i - 2j + 5k$ and $-2i + pj - qk$ are collinear,then $(p, q) = $?

Let $u$ and $v$ be two vectors. Then $|u-v|=||u|-|v||$ if and only if

If the origin is the orthocenter of an equilateral triangle whose vertices are represented by the position vectors $\vec{a}, \vec{b}, \vec{c}$,then which of the following is true?

Let $u, v$ and $w$ be non-coplanar vectors. Then the points corresponding to which of the following vectors are collinear?

Let $\overrightarrow{OA} = \hat{i} - 3\hat{j} + \hat{k}$, $\overrightarrow{OB} = \hat{i} + 3\hat{j} - 2\hat{k}$, and $\overrightarrow{OC} = 4\hat{i} + 3\hat{j} + 5\hat{k}$ be the position vectors of three points $A$, $B$, and $C$. Let $P$ be the point which divides $AB$ in the ratio $2:1$. If $l, m, n$ are the direction cosines of the vector $\overrightarrow{PC}$, then $l + 3m + 2n =$

The zero vector $(0,0,0)$ $........$