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Question

Given that P+Q+R=0. Two out of the three vectors are equal in magnitude. The magnitude of the third vector is 2 time that of the other two. Which of the following can be the angles these vectors make with each other?

A
90,135,135
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B
45,45,90
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C
30,60,90
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D
45,90,135
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Solution

The correct option is A 90,135,135
R=(P+Q)Let,P=p1^i+p2^jQ=q2^i+q2^jR=r1^i+r2^jr12+r22=2(p12+p22)=2(q12+q22)r1=(p1+q1)r2=(p2+q2)r12+r22=p12+q12+p22+q22+2p1q1+2p2q22(p12+p22)=2(p12+p22)+2p1q1+2p2q22p1q1+2p2q2=0PQ=0PQ=π2RP=θ1RQ=θ2cosθ1=RP2P=(P+Q)P2P=12θ1=3π4cosθ2=RQ2Q=(P+Q)Q2Q=12θ2=3π4

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