$A$ unit vector in $XY$-plane making an angle $45^{\circ}$ with $\hat{i}+\hat{j}$ and an angle $60^{\circ}$ with $3\hat{i}-4\hat{j}$ is

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

The position vectors of two points $A$ and $B$ are $\hat{i} + \hat{j} - \hat{k}$ and $2\hat{i} - \hat{j} + \hat{k}$ respectively. Then $|\overrightarrow{AB}| = $

Which of the following is not a property of vectors?

$ABCD$ is a tetrahedron. $\bar{i}-2\bar{j}+3\bar{k}$,$-2\bar{i}+\bar{j}+3\bar{k}$,and $3\bar{i}+2\bar{j}-\bar{k}$ are the position vectors of the points $A, B, C$ respectively. $-\bar{i}+2\bar{j}-3\bar{k}$ is the position vector of the centroid of the triangular face $BCD$. If $G$ is the centroid of the tetrahedron,then $GD=$