If $(\vec{a}-\vec{b}) \cdot(\vec{a}+\vec{b})=27$ and $|\vec{a}|=2|\vec{b}|$, then $|\vec{b}|$ is :

The unit vector in the direction of $\vec{a} + \vec{b}$ if $\vec{a} = 2\hat{i} - \hat{j} + 2\hat{k}$ & $\vec{b} = -\hat{i} + \hat{j} + -\hat{k}$ is :

If $\vec{a}$ is a non-zero vector, then always

If $\lvert\vec{a}\rvert = 4, \lvert\vec{b}\rvert = 3$ and $\lvert\vec{a}+\vec{b}\rvert = 6$, then $\lvert\vec{a}-\vec{b}\rvert =$

If $\vec a$ and $\vec b$ are two unit vectors and $|\vec a-\vec b|=\sqrt3$, then the value of $|\vec a+\vec b|$ is:

Let $\vec{a}, \vec{b}, \vec{c}$ are three vectors such that $|\vec{a}|=2, |\vec{b}|=1, |\vec{c}|=3$. If projection of $\vec{a}$ on $\vec{b}$ is equal to projection of $\vec{c}$ on $\vec{b}$ and $\vec{a}\perp\vec{c}$, then value of $|2\vec{a}+3\vec{b}-2\vec{c}|$ is

Let $\vec{a}$ be any vector such that $\vec{a}.\hat{i} = \vec{a}.(\hat{i}+\hat{j}) = \vec{a}.(\hat{i}+\hat{j}+\hat{k}) = 1$, then $\vec{a}$ is