Three vectors $\overrightarrow a ,\,\overrightarrow b $and $\overrightarrow c $ satisfy the relation $\overrightarrow a \,.\,\overrightarrow b = 0$ and $\overrightarrow a \,.\,\overrightarrow c = 0.$ The vector $\overrightarrow a $ is parallel to
$\overrightarrow b $
$\overrightarrow c $
$\overrightarrow b \,.\,\overrightarrow c $
$\overrightarrow b \times \overrightarrow c $
The two vectors have magnitudes $3$ and $5$. If angle between them is $60^o$, then the dot product of two vectors will be
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
$\hat i.\left( {\hat j \times \,\,\hat k} \right) + \;\,\hat j\,.\,\left( {\hat k \times \hat i} \right) + \hat k.\left( {\hat i \times \hat j} \right)=$
The area of the parallelogram whose sides are represented by the vectors $\hat j + 3\hat k$ and $\hat i + 2\hat j - \hat k$ is