The modulus of the vector product of two vectors is $\frac{1}{\sqrt{3}}$ times their scalar product. The angle between vectors is

If $\overrightarrow{ F }=2 \hat{ i }+\hat{ j }-\hat{ k }$ and $\overrightarrow{ r }=3 \hat{ i }+2 \hat{ j }-2 \hat{ k }$, then the scalar and vector products of $\overrightarrow{ F }$ and $\overrightarrow{ r }$ have the magnitudes respectively as

Show that the area of the triangle contained between the vectors $a$ and $b$ is one half of the magnitude of $a \times b .$

What will be the projection of vector $A=\hat{i}+\hat{j}+\hat{k}$ on vector $\vec{B}=\hat{i}+\hat{j}$.

$\hat i.\left( {\hat j \times \,\,\hat k} \right) + \;\,\hat j\,.\,\left( {\hat k \times \hat i} \right) + \hat k.\left( {\hat i \times \hat j} \right)=$

If $\vec{a}$ and $\vec{b}$ makes an angle $\cos ^{-1}\left(\frac{5}{9}\right)$ with each other, then $|\vec{a}+\vec{b}|=\sqrt{2}|\vec{a}-\vec{b}|$ for $|\vec{a}|=n|\vec{b}|$ The integer value of $n$ is . . . . . . ..