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 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

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 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 ${\rm{\vec a}}\,and\,{\rm{\vec b}}$ ?

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 $\vec{A} imes \vec{B}$?

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

The resultant of two vector of equal magnitude is twice of magnitude of either of the vectors the angle between them 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 ${\rm{\vec a}}\,and\,{\rm{\vec b}}$ ?