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Vector Algebra

Question
CBSEENMA12036278
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If space straight a with bar on top comma space straight b with bar on top comma straight c with bar on top space are non-coplanar vectors and λ is a real number, then the vectors straight a with bar on top space plus 2 straight b with bar on top space plus 3 straight c with bar on top space comma space straight lambda straight b with bar on top space plus 4 space straight c with bar on top space and space left parenthesis 2 straight lambda space minus 1 right parenthesis straight c with bar on top are non-coplanar for

  • all values of λ

  • all except one value of λ

  • all except two values of λ

  • no value of λ

Solution

C.

all except two values of λ

Condition for given three vectors to be coplanar is open vertical bar table row 1 2 3 row 0 straight lambda 4 row 0 0 cell 2 straight lambda minus 1 end cell end table close vertical bar =0
 ⇒ λ = 0, 1/2.
Hence given vectors will be non coplanar for all real values of λ except 0, 1/2.

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