$\overrightarrow A $ and $\overrightarrow B $ are two vectors given by $\overrightarrow A = 2\widehat i + 3\widehat j$ and $\overrightarrow B = \widehat i + \widehat j$. The magnitude of the component (projection) of $\overrightarrow A$ on $\overrightarrow B$ is
$5 / \sqrt 2$
$3 / \sqrt 2$
$7 / \sqrt 2$
$1 / \sqrt 2$
The area of the parallelogram having diagonals ${3\hat i}\,\, + \,\,\hat j\,\, - \,\,2\hat k$ and $\hat i\,\, - \,\,3\hat j\,\, + \;\,4\hat k$ is
Given $\left| {{\vec A_1}} \right| = 2,\,\left| {{\vec A_2}} \right| = 3$ and $\left| {{{\vec A}_1} + {{\vec A}_2}} \right| = 3$. Find the value or $\left| {\left( {{{\vec A}_1} + 2{{\vec A}_2}} \right) \times \left( {3{{\vec A}_1} - 4{{\vec A}_2}} \right)} \right|$
Projection of vector $\vec A$ on $\vec B$ is
If $\vec A,\vec B$ and $\vec C$ are vectors having a unit magnitude. If $\vec A + \vec B + \vec C = \vec 0$ then $\vec A.\vec B + \vec B.\vec C + \vec C.\vec A$ will be