If $a + b + c = 0$,then $a \times b$ is equal to:

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 $\vec{A} \perp \vec{B}$.

If $\overrightarrow{A} = 2\hat{i} + 3\hat{j} - \hat{k}$ and $\overrightarrow{B} = -\hat{i} + 3\hat{j} + 4\hat{k}$,then the projection of $\overrightarrow{A}$ on $\overrightarrow{B}$ will be:

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

Two adjacent sides of a parallelogram are represented by the two vectors $\hat{i} + 2\hat{j} + 3\hat{k}$ and $3\hat{i} - 2\hat{j} + \hat{k}$. What is the area of the parallelogram?

Three vectors $\vec{A}, \vec{B}$ and $\vec{C}$ are such that $\vec{A} \cdot \vec{B} = 0$ and $\vec{A} \cdot \vec{C} = 0$. Then $\vec{A}$ is parallel to: