If $\vec{A} = \hat{i} + \hat{j}$ and $\vec{B} = \hat{j} + \hat{k}$, then the area of the triangle formed by the vectors $\vec{A}$, $\vec{B}$ and $\vec{A} - \vec{B}$ is:

The resultant of two vector of equal magnitude is twice of magnitude of either of the vectors the angle between them is

The angle between the z-axis and the vector $\hat i + \hat j + \sqrt 2 \hat k$ is

If $\overrightarrow {{a_1}}$ and $\overrightarrow {{a_2}}$ are two non collinear unit vectors inclined at ${60^0}$ to each other then the value of $\left( {\overrightarrow {{a_1}} - \overrightarrow {{a_2}} } \right).\left( {\overrightarrow {2{a_1}} + \overrightarrow {{a_2}} } \right)$

If two vectors $\vec{A}$ and $\vec{B}$ are parallel to each other, what is the magnitude of their cross product?

If $\overrightarrow F = \widehat i + 2\widehat j - 3\widehat k$ and $\overrightarrow r = 2\widehat i - \widehat j + \widehat k$. Find $\overrightarrow r imes \overrightarrow F$

What is the angle between $\hat i + 2\hat j + 2\hat k\,and\,\,\hat i$

Projection of ${\rm{\vec P}}\,{\rm{on}}\,{\rm{\vec Q}}\;$ is

If $\overrightarrow A = 2\hat i + 3\hat j + 4\hat k\,\,and\,\,{\rm{\vec B}} = 4\hat i + 3\hat j + 2\hat k$, then angle between $\overrightarrow A$ and ${\rm{\vec B}}$ is

The angle between ${\rm{\vec A}}\;\,and\,{\rm{\vec B}}\,is\,heta$, the value of the triple product ${\rm{\vec A}}{\rm{.\vec B}} imes {\rm{\vec A}}$ is

A particle is acted upon by two forces $\vec{F_1} = 2\hat{i} + 3\hat{j} - \hat{k}$ N and $\vec{F_2} = 3\hat{i} - \hat{j} + 2\hat{k}$ N. The torque produced by these forces about the origin, if their lines of action intersect at $\vec{r} = \hat{i} - 2\hat{j} + \hat{k}$ m is: