If a,b,c ar enon-coplanar vectors and `lamda` is a real number, then the vectors `a+2b+3c,lamdab+4c and (2lamda-1)c` are non-coplanar forA. no value of `lambda`B. all except one value of `lambda`C. all except two value of `lambda`D. all values of `lambda`

If a,b,c ar enon-coplanar vectors and `lamda` is a real number, then t

1.	If a,b,c ar enon-coplanar vectors and `lamda` is a real number, then the vectors `a+2b+3c,lamdab+4c and (2lamda-1)c` are non-coplanar forA. no value of `lambda`B. all except one value of `lambda`C. all except two value of `lambda`D. all values of `lambda`
Answer» Correct Answer - C Let `alpha=a+2b+3c, beta=lambdab+4c` and `gamma (2lambda-1)c` Then, `[ alpha, beta, gamma] = \| (1, 2 , 3),(0 ,lambda, 4),(0,0,(2lambda-1))\|[ "a b c"]` `(alpha, beta, gamma] = lambda (2 lambda -1) [abc] ` Now, consider `lambda (2 lambda -1) =0` `lambda =0,(1)/(2) " " [ because [abc] ne 0]` Hence, `alpah, beta and gamma ` are non-coplanar for all value of `lambda` expcept two values `0 and (1)/(2)`.

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If a,b,c ar enon-coplanar vectors and `lamda` is a real number, then the vectors `a+2b+3c,lamdab+4c and (2lamda-1)c` are non-coplanar forA. no value of `lambda`B. all except one value of `lambda`C. all except two value of `lambda`D. all values of `lambda`

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