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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
5 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
2 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 629 Points
one year 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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