If the vectors $-3 \hat{i} + 4 \hat{j} + \lambda \hat{k}$ and $\mu \hat{i} + 8 \hat{j} + 6 \hat{k}$ are collinear, then $\lambda - \mu =$

The position vectors of $P$ and $Q$ are respectively $\overrightarrow{a}$ and $\overrightarrow{b}$. If $R$ is a point on the line $PQ$ such that $\overrightarrow{PR}=5 \overrightarrow{PQ}$,then the position vector of $R$ is

$ABC$ is an isosceles triangle right-angled at $A$. Forces of magnitude $2\sqrt{2}$,$5$,and $6$ act along $\overrightarrow{BC}$,$\overrightarrow{CA}$,and $\overrightarrow{AB}$ respectively. The magnitude of their resultant force is

If the position vectors of $A$ and $B$ are $i + 3j - 7k$ and $5i - 2j + 4k$,then the direction cosine of $\overrightarrow{AB}$ along the $y$-axis is

$D, E, F$ are points on the sides $BC, CA$ and $AB$ of a $\triangle ABC$ respectively,dividing them in the ratios $2:3, 1:2, 3:1$ internally. The lines $BE$ and $CF$ intersect on the line $AD$ at $P$. If $\overrightarrow{AP} = x_1 \overrightarrow{AB} + y_1 \overrightarrow{AC}$,then $x_1 + y_1 =$

The points in space represented by the position vectors $A = 4\hat{i}+\hat{j}+3\hat{k}$,$B = 6\hat{i}-2\hat{j}-3\hat{k}$,and $C = \hat{i}-\hat{j}-3\hat{k}$ form: