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A plane passing through three points (-l...

A plane passing through three points `(-lamda^2, 1, ) (1, -lamda^2, 1),(1, 1, lamda^2)1` also passes through `(1,1,-1)` then set consisting all the real value of `lamda` is (A) `{-sqrt3,sqrt3}` (B) `{3,-3}` (C) `{1}` (D) `{1, sqrt3, -sqrt3}`

A

{3,-3}

B

`{sqrt(3), -sqrt(3)}`

C

{1, -1}

D

`{sqrt(3)}`

Text Solution

Verified by Experts

The correct Answer is:
B
Equation of a plane passing through `(x_(1), y_(1), z_(1))(x_(2), y_(2), z_(2))` & `(x_(3), y_(3), z_(3))` is
`|(x-x_(1), y-y_(1), z-z_(1)),(x_(1)-x_(2),y_(1)-y_(2),z_(1)-z_(2)),(x_(2)-x_(3),y_(2)-y_(3),z_(2)-z_(3))| = 0`
Also it passes through `(-1, -1.1) rArr |(-1+lambda^(2), -1-1,1-1),(-lambda^(2)-1,1+lambda^(2),1-1),(1-1,-lambda^(2)-1, 1+lamda^(2))| = 0`
`rArr (1+lambda^(2))[(lambda^(2)+1)(lambda^(2)-1)-2(lambda^(2) + 1)] = 0 rArr (1+lambda^(2))^(2)[lambda^(2)-3] = 0`
`rArr lambda = +- sqrt(3)`
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