Find the value of $x$ for which $x(\hat{i}+\hat{j}+\hat{k})$ is a unit vector.

If $PQRST$ is a pentagon,then the resultant of forces $\overline{PQ}, \overline{PT}, \overline{QR}, \overline{SR}, \overline{TS}$ and $\overline{PS}$ is

If $C$ is the mid-point of the line segment $AB$ and $P$ is any point outside the line $AB$,then

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:

If $ABCD$ is a parallelogram with $AC$ and $BD$ as diagonals,then which of the following is true regarding the vector relationship between the diagonals and sides?

If $\vec{a} = a_1\hat{i} + a_2\hat{j} + a_3\hat{k}$ and $\vec{b} = b_1\hat{i} + b_2\hat{j} + b_3\hat{k}$ are parallel vectors,then which of the following is true?