Question

Vector $A$ has a magnitude of $10$ units and makes an angle of $30°$ with the positive $x-axis$. Vector $B$ has a magnitude of $20$ units· and makes an angle of $30°$ with the negative $x-axis$. What is the magnitude of the resultant between these two vectors?

• A. $20 \sqrt{3}$
• B. $35$
• C. $15 \sqrt{3}$
• D. $10 \sqrt{3}$

Answer 1

Answer: (D)

Given, $ |\vec{A}|$ = 10 units
$ |\vec{B}|$ = 20 units
Angle between $\vec{A}$ and $\vec{B}$
$\theta = 180° - 30° - 30° = 120°$
Magnitude of the resultant,
$R = \sqrt{A^2 + B^2 + 2AB \, \cos \theta}$
$=\sqrt{10^2 + 20^2 + 2 \times 10 \times 20 \, \cos \, 120^\circ}$
$ = \sqrt{100 + 400 - 200} = \sqrt{300} $
$ = 10 \sqrt{3}$ units