The angle between the two vectors $(2\hat{i} + 3\hat{j} + \hat{k})$ and $(-3\hat{i} + 6\hat{k})$ is ...... $^\circ$.

Show that the magnitude of a vector is equal to the square root of the scalar product of the vector with itself.

The angle between the vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ is $\theta$. The value of the triple product $\overrightarrow{A} \cdot (\overrightarrow{B} \times \overrightarrow{A})$ is

If $\overrightarrow{A} \times \overrightarrow{B} = \overrightarrow{C} + \overrightarrow{D},$ then select the correct alternative-

If $\vec{P} = b \hat{i} + 6 \hat{j} + \hat{k}$ and $\vec{Q} = \hat{i} - a \hat{j} + 4 \hat{k}$ are perpendicular to each other,and $3b - a = 5$,find the values of $a$ and $b$.

Find the component of vector $\vec{r}$ in the direction of vector $\vec{a}$.