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The value of lamda for which the four po...

The value of `lamda` for which the four points `2hati+3hatj-hatk,hati+2hatj+3hatk,3hati+4hatj-2hatk` and `hati-lamdahatj+6hatk` are coplanar.
a. `8`
b. `0`
c. `-2`
d. `6`

A

8

B

0

C

`-2`

D

6

Text Solution

Verified by Experts

The correct Answer is:
C
The given four poins are complanar.
`|(2,1,3,1),(3,2,4,lamda),(-1,3,-2,6),(1,1,1,0)|=0`
`implies|(2,1,3,1),(0,0,0,-(lamda+2)),(-1,3-2,6),(1,1,1,1)|=0`
Operating `(R_(2) to R_(2)-R_(1)-R_(4))`
`implies-(lamda+2)|(2,1,3),(-1,3,-2),(1,1,1)|=0implies lamda=-2`.
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