Question

The number of distinct real values of `lamda` for which the vectors `veca=lamda^(3)hati+hatk, vecb=hati-lamda^(3)hatj` and `vecc=hati+(2lamda-sin lamda)hati-lamdahatk` are coplanar is

Answer 1

Correct Answer - A
Put `Delta=0 implies lamda^(7)+lamda^(3)+2lamda-sinlamda=0`
Let `f(lamda)=lamda^(7)+lamda^(3)+2lamda-sinlamda`
`impliesf(lamda)=(7lamda^(6)+3lamda^(2)+2-coslamda) gt0, AA in R`
`thereforef(lamda)=0` has only one real solution `lamda=0`.