InterviewSolution
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InterviewSolution
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In a four-dimensional space where unit vectors along the axes are `hati,hatj,hatk and hatl, and a_(1),a_(2),a_(3),a_(4) ` are four non-zero vectors such that no vector can be expressed as a linear combination of other `(lamda-1) (a_(1)-a_(2))+mu(a_(2)+a_(3))+gamma(a_(3)+a_(4)-2a_(2))+a_(3)+deltaa_(4)=0`, thenA. `lamda=1`B. `mu=-(2)/(3)`C. `gamma=(2)/(3)`D. `delta=(1)/(3)` |
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Answer» Correct Answer - A::B::D `(lamda-1)(a_(1)-a_(2))+mu(a_(2)+a_(3))+gamma(a_(3)+a_(4)-2a_(2))+a_(3)+delta a_(4)=0` `i.e., (lamda-1)a_(1)+(1-lamda+mu-2gamma)a_(2)+(mu+gamma+1)a_(3)+(gamma+delta)a_(4)=0` Since, `a_(1),a_(2),a_(3) and a_(4)` are linearly independent, we have `lamda-1=0,1-lamda+mu-2gamma=0`, `mu+gamma+1=0 and gamma+delta=0` i.e., `lamda=1,mu=2gamma,mu+gamma+1=0,gamma+delta=0` Hence, `lamda=1,mu=-(2)/(3),gamma=-(1)/(3),delta=(1)/(3)`. |
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