InterviewSolution
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InterviewSolution
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Three vectors ` vec A, vec B` and ` vec C` add up to zero . Find which is false.A. (a) `(vec Axx vec B) xx vec C` is not zero unless ` vec B, vec c` are prallelB. (b) ` (vec Axx vec B) xx vec C` is not zero unless ` vec B, vec c` are prallelC. (c ) If `vec A.vec B, vec C` define a plane ,` ( vec A xx vec B xx vec C)` is in that planeD. (d) `(vec A xx B) . vec C = | vec A||vec B|| vec C| rarr C^2 = A^2 + B^2` |
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Answer» Correct Answer - B::D Give , `vec A+ vec B+ vec C =0`, then ` vec A, vec B` and vec C` are in one plane and are represented by the three sides of a trianle taken in one order. (i) :. ` vec B xx ( vec A+ vec B+ vec C) = vec B xx 0=0 ` or ` vec Bxx vec A + vec B+ vec Bxx vec C=0` or ` vec B xx vec A+ 0+ vec Bxx vec C=0` or ` vec A xx vec B= vec B xx vec C` :. ( vec Axx vec B) xx vec C =( vec Bxx vec C)xx vec C, It cannot be zero. If ` vec B || vec C`, then ` vec Bxx vec C =0`, then (vec Bxx vec C) xx vec C=0` ltBrgt Thus , option (a) is correct. (ii) ( vec Axx vec B) . ( vec Bxx vec C) . ( vec C=0` whatever be the positions of ` vec A, vec B` and vec C` ` If ` vec B|| vec C`, the ` vec ` vec Bxx vec C =0`, the ( vec Bxx vec C) xx vec C=0` Thus, option (b) is false ( iii) ` (vec Axx vec B) = vec D= AB sin theta hat D`. The direction of ` hat D` is perpendicular to the plane cntaning ` vec A` and ` vec B`. ( vec A xx vec B) xx cvec C = vec D xx vec C`. Its direction is in the plane of ` vec A, vec B` and vec C`. Thus, option (c ) is correct. ( iv) If ` C^@ = A^2 + B^2`, the angle between ` vec A ` and vec B` is ` 90^@`. (vec A xx vec B).vec C= ( AB sin 90^@ hat D) . vec C= AB ( hat D. vec C) = ABC cos 8=90^@=0`. Thus, option (d) is fase . ( vec A xx vec B) xx cvec C = vec D xx vec C`. Its direction is in the plane of ` vec A, vec B` and vec C`. Thus, option (c ) is correct. ( iv) If ` C^@ = A^2 + B^2`, the angle between ` vec A ` and vec B` is ` 90^@`. |
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