Question

Resultant of two vectors is $20\sqrt{3}$ and makes an angle ${30}^0$ with one of them which has magnitude $20$. The magnitude of other vector:

• A. 10
• B. 20
• C. $10\sqrt{3}$
• D. $20\sqrt{3}$

Answer 1

The correct option is B 20

Let us consider that the $3$ vectors form the 3 sides of a triangle, with
$a=20,b=20\sqrt{3}$, c = ? $\theta =30$
Using cosine rule,
$c=$ ${(a^2+b^2-2abcos\theta )}^{\frac{1}{2}}$

$c=\sqrt{{20}^2+(20\sqrt{3}{)}^2-2\times 20\times 20\sqrt{3}\times \frac{\sqrt{3}}{2}}$

$c=\sqrt{400+1200-1200}=20$.

Thus, $c=20$