InterviewSolution
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InterviewSolution
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Statement 1: Any vector in space can be uniquely written as the linear combination of three non-coplanar vectors. Stetement 2: If `veca, vecb, vecc` are three non-coplanar vectors and `vecr` is any vector in space then `[(veca,vecb, vecc)]vecc+[(vecb, vecc, vecr)]veca+[(vecc, veca, vecr)]vecb=[(veca, vecb, vecc)]vecr`A. 1B. 2C. 3D. 4 |
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Answer» Correct Answer - B Clearly statemnet -1 is true We have `vecr=xveca+yvecb+zvecc` ……………..i Taking product successively with `vecbxxvecc, veccxxveca` and `vecaxxvecb`, we obtain `x=([(vecb, vecc,vecr)])/([(veca, vecb, vecc)]),y=([(vecc, veca, vecr)])/([(veca, vecb, vecc)]),z=([(veca, vecb, vecr)])/([(veca, vecb, vecc)])` Substituting the values of `x,y,z` in (i) we get `[(vecb, vecc, vecr)]veca+[(vecc, veca, vecr)]vecb+[(veca, vecb, vecr)]vecr=[(veca, vecb, vecc)]vecr` So Statement 2 is true. But, statement2 is not a correct explanation for statement -1 |
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