$A$ unit vector does not have any .......

For the resultant of two vectors $A$ and $B$ to be maximum,the angle between them should be (in $^{\circ}$)

Find the length of the component of $\vec{a}$ along $\vec{b}$,where $\vec{a} = 4 \hat{i} + 5 \hat{j}$ and $\vec{b} = -\hat{i} + \hat{j}$.

A body cools according to Newton's law of cooling from $100^\circ C$ to $60^\circ C$ in $20$ minutes. The temperature of the surroundings being $20^\circ C$, then the total time required for the body to cool down to $30^\circ C$ is

$ABC$ 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 $n$.

Establish the following vector inequalities geometrically or otherwise:
$(a) \quad |\vec{a} + \vec{b}| \leq |\vec{a}| + |\vec{b}|$
$(b) \quad |\vec{a} + \vec{b}| \geq ||\vec{a}| - |\vec{b}||$
$(c) \quad |\vec{a} - \vec{b}| \leq |\vec{a}| + |\vec{b}|$
$(d) \quad |\vec{a} - \vec{b}| \geq ||\vec{a}| - |\vec{b}||$
When does the equality sign apply in each case?