If the vectors $2\hat{i} + 2\hat{j} - 2\hat{k}$,$5\hat{i} + y\hat{j} + \hat{k}$,and $-\hat{i} + 2\hat{j} + 2\hat{k}$ are coplanar,then the value of $y$ is:

If $\vec{a}$ and $\vec{b}$ make an angle $\cos^{-1}\left(\frac{5}{9}\right)$ with each other,then $|\vec{a}+\vec{b}|=\sqrt{2}|\vec{a}-\vec{b}|$ for $|\vec{a}|=n|\vec{b}|$. The integer value of $n$ is . . . . . . .

Given two vectors $\vec{A} = 3\hat{i} + \hat{j}$ and $\vec{B} = \hat{j} + 2\hat{k}$. Find the unit vector perpendicular to both $\vec{A}$ and $\vec{B}$.

Show that the scalar product of two vectors obeys the distributive law.

The area of the parallelogram represented by the vectors $\overrightarrow A = 2\hat i + 3\hat j$ and $\overrightarrow B = \hat i + 4\hat j$ is ....... $units^2$.

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