If three vectors $\vec{A} = \hat{i} + 2\hat{j} - \hat{k}$, $\vec{B} = -\hat{i} + \hat{j} + \hat{k}$, and $\vec{C}$ form a right-angled triangle such that $\vec{C}$ is the hypotenuse, then a possible value of $\vec{C}$ is:

If the magnitudes of scalar and vector products of two vectors and are 6 and $6\sqrt 3$ respectively, then the angle between two vectors is

$\overrightarrow A$ is a vector with magnitude A, then the unit vector $\widehat A$ in the direction of $\overrightarrow A$ is

A vector ${\rm{\vec A}}$ points vertically upwards and ${\rm{\vec B}}$ points upwards North. The vector product ${\rm{\vec A}} imes {\rm{\;\vec B}}$ is

The area of a parallelogram whose adjacent sides are given by vectors $\vec A = \hat i - 2\hat j + 3\hat k$ and $\vec B = 4\hat i + 5\hat j$ is

Two vectors having same magnitude and direction are called:

Which of the following is true about opposite vectors?

Two vectors ${\rm{\vec A}}\,and\,{\rm{\vec B}}$ are inclined to each other at an angle θ. Which of the following is the unit vector perpendicular to both ${\rm{\vec A}}\,and\,{\rm{\vec B}}$ ?

Given $heta$ is the angle between ${\rm{\vec A}}\,and\,{\rm{\vec B}}$. Then $\left| {\hat A imes \hat B\;} \right|$ is equal to

Which vector represents the position of a point in space relative to a fixed origin?

The position vectors of two points P and Q are $\vec{p}$ and $\vec{q}$ respectively. If R is a point on PQ such that PR:RQ = m:n, then the position vector of R is: