The angle made by the vector $\left( {\hat i\,\, + \;\,\hat j} \right)$ with $x-$ axis and $y$ axis is
$45^o, 60^o$
$60^o, 60^o$
$45^o, 45^o$
$60^o, 45^o$
When $\vec A.\vec B = - |A||B|,$ then
Obtain scalar product in terms of Cartesian component of vectors.
$\overrightarrow A = 2\hat i + 4\hat j + 4\hat k$ and $\overrightarrow B = 4\hat i + 2\hat j - 4\hat k$ are two vectors. The angle between them will be ........ $^o$
If $\vec A$ and $\vec B$ are perpendicular vectors and vector $\vec A = 5\hat i + 7\hat j - 3\hat k$ and $\vec B = 2\hat i + 2\hat j - a\hat k.$ The value of $a$ 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 $\left| {\left( {{{\vec A}_1} + 2{{\vec A}_2}} \right) \times \left( {3{{\vec A}_1} - 4{{\vec A}_2}} \right)} \right|$