Question:
if magnitude of a b vector is equal to a b vector , then find the angle between a vector and b vector
Answer:
Give, magnitude of a + b is equal to magnitude of a - b
=> |a - b| = |a + b|
=> |a - b|2 = |a + b|2
=> (a - b)2 = (a + b)2
=> a2 + b2 - 2a.b = a2 + b2 + 2a.b
=> - 2a.b = 2a.b
=> 2a.b + 2a.b = 0
=> 4a.b = 0
=> a.b = 0
Now,
a.b = |a|*|b|*cos θ
=> cos θ = a.b/(|a|*|b|)
=> cos θ = 0
=> cos θ = cos 90°
=> θ = 90°
So, the angle is 90°
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