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The number of distinct real values of la...

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)hatj-lamdahatk` are coplanar is

A

(a)0

B

(b)1

C

(c)2

D

(d)3

Text Solution

Verified by Experts

The correct Answer is:
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`.
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