InterviewSolution
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InterviewSolution
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Three vectors `vecA,vecB` and `vecC` add up to zero.Find which is false.A. `(AxxB)xxC` is not zero unless B, C are parallelB. `(AxxB).C` is not zero unless B, C are parallelC. If A, B, C define a plane, `(AxxB)xxC` is in that planeD. `(AxxB).C=|A||B||C| rarr C^(2)=A^(2)+B^(2)` |
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Answer» Correct Answer - B::D Given A+B+C=0 Hence, we can say that A, B and C are in one plane and are represented by the three sides of a triangle taken in one order, Now consider the options one by one. (a) We can write `Bxx(A+B+C)=Bxx0=0` `rArr " " BxxA+BxxB+BxxC=0` `rArr " " BxxA+0+BxxC=0` `rArr" "BxxA=-BxxC` `rArr " " AxxB=BxxC` `:. " " (AxxB)xxC=(BxxC)xxC` It cannot be zero. If B||C, then `BxxC=0`, than `(BxxC)xxC=0`. (b) `(AxxB).C=(BxxAC).C=0` whatever be the positions of A, B and C. If B||C, then `BxxC=0`, then `(BxxC)xxC=0`. (c) `(AxxB)=X=AB sin theta X`. The direction of X is perpendicular to the plane containing A and B. `(AxxB)xxC=XxxC`. Its direction is in the plane of A, B, and C. (d) If `C^(2)=A^(2)+B^(2)`, then angle between A and B is `90^(@)` `:. " " (AxxB).C`=(AB `sin 90^(@)` X).C=AB (X.C) `" " ABC cos 90^(@)=0` |
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