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Here X is cross product, . is dot product and A,B,C,D are non coplanar and non orthogonal vectors.D is expressed as a linear combination of A,B,C as D=aA+bB+cC.(=EQN 1) Show that coefficients are given as ratio of sclar triple product as a=(D.BXC)/A.(BXC) and so on. Here i think that we have to prove LHS=RHS. so i assumed b=(D.CXA)/(B.CXA) AND c=(D.AXB)/(C.AXB) AND I SUBSTITUTED IN EQN 1. Then i think we have to prove RHS=D so i substituted . I got [A B C] in denominator but i cant understand the numerator. Pls help. I belive we should get D([A B C]). BUT HOW?

 Here X is cross product, . is dot product and A,B,C,D are non coplanar and non orthogonal vectors.D is expressed as a linear combination of A,B,C as  D=aA+bB+cC.(=EQN 1)
Show that coefficients are given as ratio of sclar triple product as
a=(D.BXC)/A.(BXC) and so on.

Here i think that we have to prove LHS=RHS. so i assumed
b=(D.CXA)/(B.CXA) AND c=(D.AXB)/(C.AXB) AND I SUBSTITUTED IN EQN 1. Then i think we have to prove RHS=D so i substituted . I got [A B C] in denominator but i cant understand the numerator. Pls help. I belive we should get D([A B C]). BUT HOW? 

Grade:11

2 Answers

Aman Bansal
592 Points
9 years ago

Dear Parashar,

Your approach is absolutely correct and You wil get correct answer .

Best Of luck

Plz Approve the answer...!!!!

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Aman Bansal

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Parashar Chatterjee
18 Points
9 years ago

I am asking as to how to get the numerator.

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