The angle between two vectors $4\hat{i} + 3\hat{j} + \hat{k}$ and $-3\hat{i} + 2\hat{j} + 6\hat{k}$ is ....... $^o$

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

Explain the meaning of multiplication of vectors by real numbers with an example.

Consider a vector $\overrightarrow{F} = 4\hat{i} - 3\hat{j}$. Another vector that is perpendicular to $\overrightarrow{F}$ is

If the component of the vector $\vec{A}$ along the vector $\vec{B}$ is twice the component of $\vec{B}$ along $\vec{A}$, then the ratio of magnitudes of vectors $\vec{A}$ and $\vec{B}$ is

The angle between the vectors $(\hat{i} + \hat{j})$ and $(\hat{i} - \hat{k})$ is ........ $^\circ$.