Question

Two vectors have their magnitude in the ratio of $3:5$ and angle between their direction is $\pi /3$. If their resultant is $35$ units then their magnitudes are

• A. 12, 20 units
• B. 15, 25 units
• C. 18, 30 units
• D. 21, 28 units

Answer 1

The correct option is B 15, 25 units

Given: $\frac{A}{B}=\frac{3}{5}\&\theta =\frac{\pi }{3}$

$R^2=A^2+B^2+2AB\cos \theta 35=\sqrt{A^2+\frac{25}{9}{A}^2+2\frac{5}{3}{A}^2\left(\frac{1}{2}\right)}=A\sqrt{\frac{49}{9}}orA=\frac{35\times 3}{7}=15unitsB=\frac{5}{3}\times A=\frac{5}{3}\times 15=25units$