Find angle between $\vec A = 3\hat i - \hat j + 4\hat k$ and $Z-$ axis
${\tan ^{ - 1}}\,\left( {\frac{{\sqrt {22} }}{4}} \right)$
${\tan ^{ - 1}}\,\left( {\frac{{\sqrt {10} }}{4}} \right)$
${\sin ^{ - 1}}\,\left( {\frac{{\sqrt {10} }}{4}} \right)$
${\sin ^{ - 1}}\,\left( {\frac{4}{{\sqrt {26} }}} \right)$
Dot product of two mutual perpendicular vector is
If $\overrightarrow{ P }=3 \hat{ i }+\sqrt{3} \hat{ j }+2 \hat{ k }$ and $\overrightarrow{ Q }=4 \hat{ i }+\sqrt{3} \hat{ j }+2.5 \hat{ k }$ then, The unit vector in the direction of $\overrightarrow{ P } \times \overrightarrow{ Q }$ is $\frac{1}{x}(\sqrt{3} \hat{i}+\hat{j}-2 \sqrt{3} \hat{k})$. The value of $x$ is
Consider a vector $\overrightarrow F = 4\hat i - 3\hat j.$ Another vector that is perpendicular to $\overrightarrow F $ is
$\hat i.\left( {\hat j \times \,\,\hat k} \right) + \;\,\hat j\,.\,\left( {\hat k \times \hat i} \right) + \hat k.\left( {\hat i \times \hat j} \right)=$