If the projection of $2 \hat{i}+4 \hat{j}-2 \hat{k}$ on $\hat{i}+2 \hat{j}+\alpha \hat{k}$ is zero. Then, the value of $\alpha$ will be.

If $|\vec A \times \vec B| = \sqrt 3 \vec A.\vec B,$ then the value of$|\vec A + \vec B|$ is

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

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

The angle between two vectors given by $6\hat i + 6\hat j - 3\hat k$ and $7\hat i + 4\hat j + 4\hat k$ is

Show that the scalar product of two vectors obeys the law of distributive.