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 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 two vectors $\overrightarrow{A} = 5\hat{i} + 5\hat{j}$ and $\overrightarrow{B} = 5\hat{i} - 5\hat{j}$ will be ....... $^\circ$.

The unit vector perpendicular to the two vectors $(2\hat{i} + 3\hat{j} + \hat{k})$ and $(\hat{i} - \hat{j} + 2\hat{k})$ is:

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

If $\overrightarrow{A}$ and $\overrightarrow{B}$ are two vectors,then which of the following are correct?
$(a) \ (\overrightarrow{A} \times \overrightarrow{B}) \perp \overrightarrow{A}$
$(b) \ (\overrightarrow{A} \times \overrightarrow{B}) \perp \overrightarrow{B}$
$(c) \ (\overrightarrow{A} \times \overrightarrow{B}) \perp (\overrightarrow{A} + \overrightarrow{B})$
$(d) \ (\overrightarrow{A} \times \overrightarrow{B}) \perp (\overrightarrow{A} - \overrightarrow{B})$
$(e) \ (\overrightarrow{A} \times \overrightarrow{B}) \perp (\overrightarrow{A} \cdot \overrightarrow{B})$