If $p = 7i - 2j + 3k$ and $q = 3i + j + 5k$,then $|p - 2q| = \dots$

Let $\vec{v}$ be a vector in the plane such that $|\vec{v} - \hat{i}| = |\vec{v} - 2\hat{j}| = |\vec{v} - \hat{j}|$. Then,$|\vec{v}|$ lies in the interval

Let $\overrightarrow{a}$ and $\overrightarrow{b}$ be two vectors such that $|\overrightarrow{a}| = 2$ and $|\overrightarrow{b}| = 3$. Then the ratio of the projection of $\overrightarrow{a}$ on $\overrightarrow{b}$ to that of $\overrightarrow{b}$ on $\overrightarrow{a}$ is:

Classify the following as scalar or vector quantities:
Time period

If $\vec{a}, \vec{b}, \vec{c}$ are the position vectors of points $A, B, C$ respectively,and $D$ is the midpoint of $BC$,then $\vec{AD} = \dots$

If the position vectors of three points are $a$,$b$,and $(3a - 2b)$,then these points are .....