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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

0

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
A
Put `Delta=0`
`rArr lambda^(7)+lambda^(3)-sinlambda=0`
Let `f(lambda)=(7lambda^(6)+3lambda^(2)+2-coslambda) gt 0` in R
`therefore f(lambda)=0` has only one real solution `lambda=0`
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