Two vectors `vec(a)` and `vec(b)` are such that `|vec(a)+vec(b)|=|vec(a)-vec(b)|`. What is the angle between `vec(a)` and `vec(b)`?

Explanation

Refer to Fig. 2 (c ) . 61,`
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Here, ` | vec A| =OP, |vec B| =OQ =Ps`,
` | vec R| = OS= B//2`
In Delta OPS, (OP)^(2) + (OS)^(2)= (PS)^(2)`
` A^(2) + (B//2) ^(2) =B ^(2) or A^(2) =3/4 B^(2) or A= (sqrt3)/2 B`
Let ` /_OPS=theta, then tan theta (OS)/(OP) =(B//2) /A`
or ` tan theta = B/(2 A) =B/(2 xx (sqrt 3//2)B) =1/(sqrt 3) = tan 30^(@)`
or ` theta =30^(@)`
Therefore angle between ` vec A and vec B`
` beta =(180^(@)-theta )=(18^(@) -30&(@) =150^(@)`.