InterviewSolution
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InterviewSolution
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Two vectors `vec A and vecB` have equal magnitudes.If magnitude of `(vecA+vecB)` is equal to n times ofthe magnitude of `(vecA-vecB)` then the anglebetween `vecA and vecB` is :-A. `cos^(-1) ((n - 1)/(n + 1))`B. `cos^(-1) ((n^(2) - 1)/(n^(2) + 1))`C. `sin^(-1) ((n - 1)/(n + 1))`D. `sin^(-1) ((n^(2) - 1)/(n^(2) + 1))` |
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Answer» Correct Answer - B Let `theta` be the angle between `vec(A)` and `vec(B)` `|vec(A) + vec(B)| = n|vec(A) - vec(B)| rArr sqrt(A^(2) + B^(2) + 2 AB cos theta)` `= n sqrt(A^(2) + B^(2) + 2 AB cos (180 - theta))` `|vec(A)| = |vec(B)| = A = B = x` `2x^(2) ( 1 + cos theta) = n^(2) . 2x^(2) ( 1 - cos theta)` `1 + cos theta = n^(2) . n^(2) cos theta` `(1 + n^(2)) cos theta = n^(2) - 1` `cos theta = (n^(2) - 1)/(n^(2) + 1)` `theta = cos^(-1) ((n^(2) - 1)/(n^(2) + 1))` |
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