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:

$\overrightarrow{A}$ and $\overrightarrow{B}$ are two vectors given by $\overrightarrow{A} = 2\widehat{i} + 3\widehat{j}$ and $\overrightarrow{B} = \widehat{i} + \widehat{j}$. The magnitude of the component (projection) of $\overrightarrow{A}$ on $\overrightarrow{B}$ is

If $\overrightarrow A = 3\hat i + \hat j + 2\hat k$ and $\overrightarrow B = 2\hat i - 2\hat j + 4\hat k$,then the value of $|\overrightarrow A \times \overrightarrow B |$ will be:

$\vec{A}$ is a vector quantity such that $|\vec{A}| =$ nonzero constant. Which of the following expressions is true for $\vec{A}$?

Find the angle in $^o$ between two vectors $\overrightarrow{A} = 2\hat{i} + 4\hat{j} + 4\hat{k}$ and $\overrightarrow{B} = 4\hat{i} + 2\hat{j} - 4\hat{k}$.

Let $\vec{P} = P \sin \theta \hat{i} - P \cos \theta \hat{j}$ be any vector. Another vector $\vec{Q}$ which is perpendicular to $\vec{P}$ is