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Question

Three vectors P, Q and R are such that |P|=|Q|,|R|=2|P| and P+Q+R=0. The angle between P and Q,Q and R, and P and R are

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

The correct option is A 90,135,135
Vectors P+Q+R=0
Given |P|=|Q| and |R|=2|P|
Let ϕ be the angle between vectors P and Q.
So, using vector addition P+Q=R
|P+Q|2=|R|2=|R|2
|P|2+|Q|2+2|P||Q|×cosϕ=2|P|2
Hence, cosϕ=0ϕ=π2=90

As P and Q vectors of equal magnitude, R will be at π4 angle from either P and Q. So R will be at 180 from - R.
Angle between Q and R=18045=135
Angle between vectors R and P=135

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