Home
Class 12
MATHS
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)hati-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`
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    CENGAGE|Exercise Question Bank|30 Videos

  • LOGARITHM AND ITS APPLICATIONS

    CENGAGE|Exercise Subjective Type|9 Videos

Similar Questions

Explore conceptually related problems

The number of distinct values of lamda , for which the vectors -lamda^(2)hati+hatj+hatk, hati-lamda^(2)hatj+hatk and hati+hatj-lamda^(2)hatk are coplanar, is

The number of distinct real values of lamda for which the vectors -lamda^2hati+hatj+hatk, hati-lamda^2hatj+hatk and hati+hatj-lamda^2 hatk are coplanar is (A) zero (B) one (C) two (D) three

The value of lamda for which the vectors 3hati-6hatj+hatkand2hati-4hatj+lamdahatk parallel, is

Find the value of lamda such that the vectors veca=2hati+lamdahatj+hatkandvecb=hati+2hatj+3hatk are orthogonal.

For what value of lamda are the vectors veca=2hati+lamda hatj+hatk and vecb=hati-2hatj+3hatk perpendicular to each other ?

For what values of lamda are the vectors lamdahati+2hatj+hatk,3hati+2hatj,lamda i+j are coplanar.

Find the value of lamda so that the two vectors 2hati+3hatj-hatk and -4hati-6hatj+lamda hatk are parallel

If veca = hati - hatj + hatk, vecb= 2 hati + hatj -hatk and vec c = lamda hati -hatj+ lamda hatk are coplanar, find the value of lamda.