If $a = \hat{i} + 4 \hat{j}$, $b = 2 \hat{i} - 2 \hat{j}$, and $c = 5 \hat{i} + 9 \hat{j}$, then $c$ is equal to:

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

If $p = 7i - 2j + 3k$ and $q = 3i + j + 5k,$ then the magnitude of $p - 2q$ is

If $\bar{a}=\hat{\imath}+\hat{\jmath}+\hat{k}, \bar{b}=2 \hat{\imath}-2 \hat{\jmath}+2 \hat{k}, \bar{c}=2 \hat{\imath}+3 \hat{\jmath}+2 \hat{k}$ are three vectors such that $l \bar{a}+m \bar{b}+n \bar{c}=\overline{0}$,then the values of $l, m, n$ are respectively

$A$ vector in the direction of $v = 2\hat{i} + 3\hat{j} + \hat{k}$ with magnitude $\sqrt{7}$ is

If $A(2 \hat{i} + \hat{j} - \hat{k})$, $B(\lambda \hat{i} + 5 \hat{j} + 4 \hat{k})$, $C(-4 \hat{i} + 3 \hat{j} + 2 \hat{k})$ and $D(-\hat{i} - 2 \hat{j} + 3 \hat{k})$ are four points in space such that $\overrightarrow{AB} = x \overrightarrow{AC} + y \overrightarrow{AD}$ for some real numbers $x \neq 0, y \neq 0$, then $17(\lambda + 9) =$ ?