$A$ vector perpendicular to the vector $(4 \hat{i}-3 \hat{j})$ is

The area of the parallelogram formed by vectors $\vec{P} = 2\hat{i} - \hat{j} + 5\hat{k}$ and $\vec{Q} = 3\hat{i} - 2\hat{j} + 4\hat{k}$ is

If $|A|=2, |B|=5$ and $|A \times B|=8$. If the angle between $A$ and $B$ is acute,then $A \cdot B$ is

Find the angle between the two vectors: $\vec{a}=3 \hat{i}+2 \hat{j}+5 \hat{k}$ and $\vec{b}=5 \hat{i}+3 \hat{j}+\hat{k}$.

If $\vec{A} = 4\hat{i} + n\hat{j} - 2\hat{k}$ and $\vec{B} = 2\hat{i} + 3\hat{j} + \hat{k}$,find the value of $n$ such that $\vec{A} \perp \vec{B}$.

What is the angle between $(\overrightarrow P + \overrightarrow Q)$ and $(\overrightarrow P \times \overrightarrow Q)$?