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If veca, vecb, vecc are non-coplanar vec...

If `veca, vecb, vecc` are non-coplanar vectors and `lamda` is a real number, then the vectors `veca + 2 vecb + 3 vec c , lamda vecb + mu vec c and (2 lamda -1) vecc` ar non-coplanar for:

A

all value of `lamda`

B

all except one value of `lamda`

C

all except two value of `lamda`

D

no value of `lamda`

Text Solution

Verified by Experts

The correct Answer is:
C
The three vectors (a+2b+3c),`(lamdab+4c) annd (2lamda-1)`c are non-coplanar, if
`|(1,2,3),(0,lamda,4),(0,0,2lamda-1)|ne0`
`implies (2lamda-1)(lamda) ne0`
`implies lamda ne0,(1)/(2)`
So, these three vectors are non-coplanar for all except two values of `lamda`.
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