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Question

Maximum and minimum magnitudes of the resultant of two vectors of magnitudes P and Q are in the ratio 3:1. Which of the following relations is true?

A
P=Q
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B
P=2Q
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C
PQ=1
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D
none of the above
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Solution

The correct option is B P=2Q
Step 1: Resultant of two vectors
Let θ be the angle between two vectors.
Resultant of P and Q: R=P2+Q2+2PQcosθ

Step 2: Condition for maximum and minimum resultant
For maximum resultant, the vectors are parallel i.e. θ=0

Rmax=P2+Q2+2PQcos0o=(P+Q)2

Rmax=P+Q

For minimum resultant, the vectors are antiparallel i.e. θ=180o

Rmin=P2+Q2+2PQcos180=(PQ)2

Rmin=PQ

Step 3: Calculation
Given: RmaxRmin=31

P+QPQ=31

P+Q=3P3Q
P=2Q

Hence, option B is correct.

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