1.

If a, b and c are non-coplanar vectors and r is a real number, then the vectors a+2b+3c, lambdab+4c and (2lambda-1)c are non-coplanar for

Answer»

no value of `lambda`
all except ONE value of `lambda`
all except two value of `lambda`
all values of `lambda`

SOLUTION :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` expcepttwo values`0 and (1)/(2)`.


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