Can the resultant of $2$ vectors be zero?

Two vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ are at an angle of $60^{\circ}$ with each other. Their resultant makes an angle of $45^{\circ}$ with $\overrightarrow{a}$. If $|\overrightarrow{b}| = 2 \text{ units}$,then $|\overrightarrow{a}|$ is:

$A$ car travels $6 \, km$ at an angle of $45^\circ$ north of east and then travels $4 \, km$ at an angle of $135^\circ$ north of east. How far is the final point from the starting point? What angle does the straight line joining its initial and final position make with the east?

Prove the associative law of vector addition.

What is the angle between $\overrightarrow P$ and the resultant of $(\overrightarrow P + \overrightarrow Q)$ and $(\overrightarrow P - \overrightarrow Q)$?

Given $\vec{A}=(2 \hat{i}-3 \hat{j}+\hat{k})$,$\vec{B}=(3 \hat{i}+\hat{j}-2 \hat{k})$ and $\vec{C}=(3 \hat{i}+2 \hat{j}+\hat{k})$. The value of $(\vec{A}+\vec{B}) \cdot \vec{C}$ will be