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