InterviewSolution
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InterviewSolution
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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)`?A. `30^(@)`B. `45^(@)`C. `60^(@)`D. `90^(@)` |
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Answer» Correct Answer - D Let `theta` be the angle between the vectors `vec(A)` and `vec(B)`. Then `|vec(A)+vec(B)|= sqrt(A^(2)+B^(2)+2AB cos theta)` `|vec(A)-vec(B)|= sqrt(A^(2)+B^(2)-2AB cos theta)` `|vec(A)+vec(B)|=|vec(A)-vec(B)|` `:. sqrt(A^(2)+B^(2)+2ABcos theta)=sqrt(A^(2)+B^(2)-2AB cos theta)` Squarung both side, we get `A^(2)+B^(2)+2AB cos theta= A^(2)+B^(2)-2AB cos theta` `4AB cos theta=0` `:. cos theta=0 or theta= (pi)/2` |
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