The area of the parallelogram formed by the vectors $\vec{A} = 3\hat{i} + \hat{j} + 2\hat{k}$ and $\vec{B} = \hat{i} - 2\hat{j} - 4\hat{k}$ is:

The vectors ${\rm{\vec a}}\,and\,{\rm{\vec b}}$ are such that $\left| {{\rm{\vec a}} + {\rm{\vec b}}} \right| = \left| {{\rm{\vec a}} - {\rm{\vec b}}} \right|$. What is the angle between ${\rm{\vec a}}\,and\,{\rm{\vec b}}$ ?

If  ${\rm{\vec P}} = 4{\rm{\hat i}} - 2{\rm{\hat j}} + 6{\rm{\hat k\;}}\,\,\,{\rm{and}}\,\,{\rm{\vec Q}} = {\rm{\hat i}} - 2{\rm{\hat j}} - 3{\rm{\hat k}}$ , then the angle which ${\rm{\vec P}} + {\rm{\vec Q}}$ makes with x-axis is

If  ${\rm{\vec P}} = 4{\rm{\hat i}} - 2{\rm{\hat j}} + 6{\rm{\hat k\;}}\,\,\,{\rm{and}}\,\,{\rm{\vec Q}} = {\rm{\hat i}} - 2{\rm{\hat j}} - 3{\rm{\hat k}}$ , then the angle which ${\rm{\vec P}} + {\rm{\vec Q}}$ makes with x-axis is

If ${{\rm{\vec A}}_1}\,and\,{{\rm{\vec A}}_2}$ are two non-collinear unit vectors and if $\left| {{{{\rm{\vec A}}}_1} + {{{\rm{\vec A}}}_2}} \right| = \sqrt 3$, then the value of $\left( {{{{\rm{\vec A}}}_1} - {{{\rm{\vec A}}}_2}} \right).\left( {2{{{\rm{\vec A}}}_1} + {{{\rm{\vec A}}}_2}} \right)$

The vectors ${\rm{\vec a}}\,and\,{\rm{\vec b}}$ are such that $\left| {{\rm{\vec a}} + {\rm{\vec b}}} \right| = \left| {{\rm{\vec a}} - {\rm{\vec b}}} \right|$. What is the angle between ${\rm{\vec a}}\,and\,{\rm{\vec b}}$ ?

If  ${\rm{\vec P}} = 4{\rm{\hat i}} - 2{\rm{\hat j}} + 6{\rm{\hat k\;}}\,\,\,{\rm{and}}\,\,{\rm{\vec Q}} = {\rm{\hat i}} - 2{\rm{\hat j}} - 3{\rm{\hat k}}$ , then the angle which ${\rm{\vec P}} + {\rm{\vec Q}}$ makes with x-axis is

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

Given two vectors $\vec{A}$ and $\vec{B}$ such that $|\vec{A}| = 3$, $|\vec{B}| = 4$ and $|\vec{A} + \vec{B}| = 5$. What is the magnitude of $\vec{A} imes \vec{B}$?

If ${{\rm{\vec A}}_1}\,and\,{{\rm{\vec A}}_2}$ are two non-collinear unit vectors and if $\left| {{{{\rm{\vec A}}}_1} + {{{\rm{\vec A}}}_2}} \right| = \sqrt 3$, then the value of $\left( {{{{\rm{\vec A}}}_1} - {{{\rm{\vec A}}}_2}} \right).\left( {2{{{\rm{\vec A}}}_1} + {{{\rm{\vec A}}}_2}} \right)$

The vectors ${\rm{\vec a}}\,and\,{\rm{\vec b}}$ are such that $\left| {{\rm{\vec a}} + {\rm{\vec b}}} \right| = \left| {{\rm{\vec a}} - {\rm{\vec b}}} \right|$. What is the angle between ${\rm{\vec a}}\,and\,{\rm{\vec b}}$ ?