If $|\bar{a}|=3, |\bar{b}|=4, |\bar{a}-\bar{b}|=5$,then $|\bar{a}+\bar{b}|=$

Classify the following as scalar or vector quantity:
distance

The components of a vector $\vec{a}$ with respect to a rectangular Cartesian system are $2p$ and $1$. The system is rotated about the origin through a certain angle in the counter-clockwise direction. If the components of $\vec{a}$ with respect to the new system are $p + 1$ and $1$,then:

If $\vec{AB} = 3 \hat{i} + 5 \hat{j} + 4 \hat{k}$ and $\vec{AC} = 5 \hat{i} - 5 \hat{j} + 2 \hat{k}$ represent the sides of triangle $ABC$,then the length of the median through $A$ is

Find the vector $\vec{c}$ which is in the direction of the internal angle bisector of the vectors $\vec{a} = 7\hat{i} - 4\hat{j} - 4\hat{k}$ and $\vec{b} = -2\hat{i} - \hat{j} + 2\hat{k}$ with $|\vec{c}| = 5\sqrt{6}$.

Let $\vec{a} = \hat{i} + 2\hat{j}$ and $\vec{b} = 2\hat{i} + \hat{j}$. Is $|\vec{a}| = |\vec{b}|$? Are the vectors $\vec{a}$ and $\vec{b}$ equal?