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Three vectorsvec A, vec B andvec C add up to zero . Find which is false. |
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Answer» (a)`(vec Axx vec B) XX vec C` is not zero unless ` vec B, vec c` are prallel (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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