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Vectors a,b,c are such that a+b+c=0 |a|=3 |b|=5 |c|=7 find angle between a&b

Vectors a,b,c are such that a+b+c=0 |a|=3 |b|=5 |c|=7  find angle between a&b

Grade:12

1 Answers

Abhi mishra
37 Points
3 years ago
Given,
|a|=3,|b|=5,|c|=7 and a+b+c=0
a+b=-c
squaring both sides we get,
|a+b|2=|-c|2
|a|2+|b|+ 2a.b=|-c|2
9+25+2a.b = 49
2a.b=49-34
2a.b=15
a.b=15/2
We know that 
a.b=|a| |b|cos\Theta
Hence,
15/2=3x5 cos\Theta
15/2=15 cos\Theta
1/2=cos\Theta
\Theta=cos-1 1/2

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