Question

Given both vector A & B have the same magnitude of 1 unit. Find $\overrightarrow{c}$ such that $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=0$?

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Given magnitude of A & B are 1

Vector B = $-1sin{30}^{\circ }\hat{i}+1cos{30}^{\circ }\hat{j}$

=$-\frac{1}{2}\hat{i}+\frac{\sqrt{3}}{2}\hat{j}$

Vector A = $-1cos{30}^{\circ }\hat{i}+1sin{30}^{\circ }\hat{j}$

$\frac{\sqrt{3}}{2}\hat{i}+\frac{1}{2}\hat{j}$

$\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C}=0$

$\Rightarrow \overrightarrow{C}=-\overrightarrow{A}-\overrightarrow{B}$

=$-(\frac{-\sqrt{3}}{2}\hat{i}+\frac{1}{2}\hat{j})-(-\frac{1}{2}\hat{i}-\frac{\sqrt{3}}{2}\hat{j})$

=$(\frac{\sqrt{3}}{2}+\frac{1}{2})\hat{i}-(-\frac{1}{2}+\frac{\sqrt{3}}{2})\hat{j}$

$\overrightarrow{C}=\left(\frac{\sqrt{3}+1}{2}\right)\hat{i}+\frac{(\sqrt{3}-1)}{2}\hat{j}$