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Question

The scalars l and m such that la+mb=c where a,b and c are given vectors, are equal to


A

l=(c×b).(a×b)|a×b|2 ; m=(c×a).(b×a)|b×a|2

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B

l=(c×b).(a×b)|a×b| ; m=(c×a).(b×a)|b×a|

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C

l=|c×b|2|a×b|2 ; m=|c×a|2|b×a|2

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D

l=|c×a|2|b×a|2 ; m=|c×b|2|a×b|2

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Solution

The correct option is A

l=(c×b).(a×b)|a×b|2 ; m=(c×a).(b×a)|b×a|2


la+mb=c
(la+mb)×b=c×bla×b=c×b
Take dot product with a×b
l|a×b|2=(c×b).(a×b)l=(c×b).(a×b)|a×b|2
Similarly, m=(c×a).(b×a)|b×a|2


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