Find $|\vec{a}-\vec{b}|$,if two vectors $\vec{a}$ and $\vec{b}$ are such that $|\vec{a}|=2, |\vec{b}|=3$ and $\vec{a} \cdot \vec{b}=4$.

Let the vectors $\overrightarrow{AB} = 2\hat{i} + 2\hat{j} + \hat{k}$ and $\overrightarrow{AC} = 2\hat{i} + 4\hat{j} + 4\hat{k}$ be two sides of a triangle $ABC$. If $G$ is the centroid of $\triangle ABC$, then $\frac{27}{7}(\overrightarrow{AG})^2 + 5 =$

If $\hat{x}, \hat{y},$ and $\hat{z}$ are three unit vectors in three-dimensional space,then find the minimum value of $|\hat{x} + \hat{y}|^2 + |\hat{y} + \hat{z}|^2 + |\hat{z} + \hat{x}|^2$.

Classify the following as scalar or vector quantity:
distance

If the vectors $-3 \hat{i} + 4 \hat{j} + \lambda \hat{k}$ and $\mu \hat{i} + 8 \hat{j} + 6 \hat{k}$ are collinear, then $\lambda - \mu =$

If $\vec{a}$ and $\vec{b}$ are two non-collinear vectors,then $|\vec{b}| \vec{a} + |\vec{a}| \vec{b}$ represents: