Consider two vectors $\vec{F}_1 = 2\hat{i} + 5\hat{k}$ and $\vec{F}_2 = 3\hat{j} + 4\hat{k}$. The magnitude of the scalar product of these vectors is

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

Two forces $\vec F_1 = 5\hat i + 10\hat j - 20\hat k$ and $\vec F_2 = 10\hat i - 5\hat j - 15\hat k$ act on a single point. The angle between $\vec F_1$ and $\vec F_2$ is nearly . . . . . . $^\circ$.

If $\vec{A} + \vec{B} + \vec{C} = 0$,then $\vec{A} \times \vec{B}$ is equal to:

If a vector $\vec A$ is parallel to another vector $\vec B$,then the resultant of the vector $\vec A \times \vec B$ will be equal to

Two unit vectors $\hat{a}_{1}$ and $\hat{a}_{2}$ are inclined to each other at an angle $\theta$. If $|\hat{a}_{1}-\hat{a}_{2}|=\sqrt{3}$,then the value of $(\hat{a}_{1}-\hat{a}_{2}) \cdot (2\hat{a}_{1}-\hat{a}_{2})$ is: