Distinguish between a vector quantity and a scalar quantity.

What is the magnitude of a new vector obtained by multiplying a vector $\vec{A}$ by $-\frac{3}{2}$?

State with reasons,whether the following algebraic operations with scalar and vector physical quantities are meaningful:
$(a)$ adding any two scalars,
$(b)$ adding a scalar to a vector of the same dimensions,
$(c)$ multiplying any vector by any scalar,
$(d)$ multiplying any two scalars,
$(e)$ adding any two vectors,
$(f)$ adding a component of a vector to the same vector.

$ABC$ is an equilateral triangle. The length of each side is $a$ and the centroid is point $O$. If $\overrightarrow{AB} + \overrightarrow{AC} = n \overrightarrow{AO}$,then find the value of $n$.

Given $A = 3\hat{i} + 4\hat{j}$ and $B = 7\hat{i} + 24\hat{j}$,find a vector that has the same magnitude as $B$ and is parallel to $A$.

$A$ physical quantity which has a direction: