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If |A| = |B| = |A+B|, then the angle between vectors A ad B is????

If |A| = |B| = |A+B|, then the angle between vectors A ad B is????

Grade:11

3 Answers

Vikas TU
14149 Points
7 years ago
|B| = |A+B|
squaring both sides,
|B|^2 = |A|^2 + |B|^2 + 2A.B
|A|^2 + 2A.B = 0
A.B = -|A|^2/2  = -|B|^2/2................(1)
 
Angle b/w A and B  vectors = >
cos@ =  A.B/|A|^2 =   -|A|^2/2*|A|^2 = -1/2 { From eqn. (1)
@ = 120 degree.
 
Biswajeet Behera
13 Points
5 years ago
If |A+B| and |A| and |B| are the sides of a triangle then the form a equilateral triangle and angles are 60degrees each angle will form 120 degrees according to triangle law.
Kushagra Madhukar
askIITians Faculty 628 Points
3 years ago
Dear student,
Please find the answer to your question.
 
|B| = |A+B|
squaring both sides,
|B|^2 = |A|^2 + |B|^2 + 2A.B
|A|^2 + 2A.B = 0
A.B = -|A|^2/2  = -|B|^2/2................(1)
 
Angle b/w A and B  vectors = >
cos@ =  A.B/|A|^2 =   -|A|^2/2*|A|^2 = -1/2 { From eqn. (1)
@ = 120 degree.
 
Thank and regards,
Kushagra

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