Question

Maximum and minimum magnitudes of the resultant of two vectors of magnitudes $P$ and $Q$ are found to be in the ratio of $3:1$. Then

• A. $P=Q$
• B. $P=2Q$
• C. $P=4Q$
• D. $P=Q/3$

Answer 1

The correct option is B $P=2Q$


Condition for minimum magnitude of resultant vector , angle of vector should be $(\theta ={180}^{\text{o}}),R_{min}=P-Q$

Condition for maximum magnitude of resultant vector , angle of vector should be $(\theta =0^{\text{o}}),R_{max}=P+Q$

$\frac{R_{max}}{R_{min}}=\frac{P+Q}{P-Q}=\frac{3}{1}$
Dividing the numerator and the denominator by $Q$ on LHS
$\frac{P/Q+1}{P/Q-1}=\frac{3}{1}$
$\Rightarrow \frac{P}{Q}+1=\frac{3P}{Q}-3$
$\Rightarrow \frac{P}{Q}=\frac{4}{2}=2$

$\Rightarrow P=2Q$

Hence option B is the correct answer.