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The variable plane (2lambda+1)x+(3-lambd...

The variable plane `(2lambda+1)x+(3-lambda)y+z=4` always passes through the line

A

`x/0=y/0=(z-4)/1`

B

`x/1=y/2=(z-4)/-3`

C

`x/1=y/1=(z-4)/-7`

D

`x/1=y/2=(z-4)/-7`

Text Solution

Verified by Experts

The correct Answer is:
D
The plane is `x+3y+z-4+lambda(2x-y)=0`
This is always passes through the line of intersection of the planes `x+3y+z=4=0` and `2x-y=0`
Now, `2x-y=0 rArr x/1=y/2`
`therefore x+3y+z-4=0`
`rArr x+3.2x+z-4=0`
`rArr x+3.2x+z-4=0`
`rArr 7x+z-4=0`
`rArr 7x = -(z-4)`
`rArr x/1=(z-4)/-7`
`therefore` line is `x/1=y/2=(z-4)/-7`
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CENGAGE-EQUATION OF PLANE AND ITS APPLICATIONS -I -DPP 3.3
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