If a vector $2\hat i + 3\hat j + 8\hat k$ is perpendicular to the vector $4\hat j - 4\hat i + \alpha \hat k$,then the value of $\alpha$ 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 ....... $^\circ$.

What is the product of two vectors if they are parallel or antiparallel?

If $\vec{A}, \vec{B}$ and $\vec{C}$ are vectors having unit magnitude. If $\vec{A} + \vec{B} + \vec{C} = \vec{0}$,then $\vec{A} \cdot \vec{B} + \vec{B} \cdot \vec{C} + \vec{C} \cdot \vec{A}$ will be:

The angle between two vectors $4\hat{i} + 3\hat{j} + \hat{k}$ and $-3\hat{i} + 2\hat{j} + 6\hat{k}$ is ....... $^o$

Two vectors $\vec{A} = 3\hat{i} + \hat{j}$ and $\vec{B} = \hat{j} + 2\hat{k}$ are given. Find the component of $\vec{A}$ along $\vec{B}$ in vector form.