State and explain the characteristics of vector product of two vectors. 

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 $\left| {\left( {{{\vec A}_1} + 2{{\vec A}_2}} \right) \times \left( {3{{\vec A}_1} – 4{{\vec A}_2}} \right)} \right|$

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

If $\overrightarrow {\rm A} = 2\hat i + 3\hat j – \hat k$ and $\overrightarrow B = – \hat i + 3\hat j + 4\hat k$ then projection of $\overrightarrow A $ on $\overrightarrow B $ will be

$\vec{A}$ is a vector quantity such that $|\vec{A}|=$ nonzero constant. Which of the following expressions is true for $\vec{A}$ $?$