If $2 \overrightarrow{a} + 3 \overrightarrow{b} - 5 \overrightarrow{c} = \overrightarrow{0}$,then the ratio in which $\overrightarrow{c}$ divides $\overrightarrow{AB}$ is

If the vectors $\vec{AB} = -3\hat{i} + 4\hat{k}$ and $\vec{AC} = 5\hat{i} - 2\hat{j} + 4\hat{k}$ are the sides of a $\triangle ABC$,then the length of the median through $A$ is

If $P(1, 3, -7)$ and $Q(5, -2, 4)$,then $|\vec{PQ}| = \dots$

Find the unit vector in the direction of the sum of the vectors,$\vec{a}=2 \hat{i}+2 \hat{j}-5 \hat{k}$ and $\vec{b}=2 \hat{i}+\hat{j}+3 \hat{k}$.

If the position vectors of the points $A, B, C$ are $i + j$,$i - j$,and $a i + b j + c k$ respectively,then the points $A, B, C$ are collinear if

Let $\overrightarrow{a}$ and $\overrightarrow{b}$ be two vectors such that $|\overrightarrow{a}| = 2$ and $|\overrightarrow{b}| = 3$. Then the ratio of the projection of $\overrightarrow{a}$ on $\overrightarrow{b}$ to that of $\overrightarrow{b}$ on $\overrightarrow{a}$ is: