The number of unit vectors of the form $a \hat{i} + b \hat{j} + c \hat{k}$,where $a, b, c \in W$ is

Classify the following measure as a scalar or a vector:
$40^{o}$

If $3 \hat{i}-5 \hat{j}+2 \hat{k}, 7 \hat{i}+2 \hat{j}-4 \hat{k}, \hat{i}-3 \hat{j}+4 \hat{k}$ and $-7 \hat{i}-17 \hat{j}+16 \hat{k}$ are position vectors of the points $A, B, C$ and $D$ respectively, then the angle between $\overrightarrow{AB}$ and $\overrightarrow{CD}$ is

In a parallelogram $ABCD$,if $\vec{AC}$ and $\vec{BD}$ are the diagonals,then which of the following is equal to $\vec{AC} + \vec{BD}$?

If $2 \hat{i}+4 \hat{j}-5 \hat{k}$, $\hat{i}+\hat{j}+\hat{k}$, and $\hat{j}+2 \hat{k}$ are the position vectors of the vertices $A$, $B$, and $C$ of a triangle respectively, then a unit vector along the median drawn through the vertex $A$ is

$A$ vector $\bar{a}$ has components $1$ and $2p$ with respect to a rectangular Cartesian system. This system is rotated through a certain angle about the origin in the counter-clockwise sense. If,with respect to the new system,$\bar{a}$ has components $1$ and $(p+1)$,then: