The variable plane `(2lamda + 1)x + (3 – lamda)`y + z = 4 always passes through the line:–
| A. |
`x/0=y/0=(z+4)/1` |
| B. |
`x/1=y/2=z/-3` |
| C. |
`x/1=y/1=(z-4)/-7` |
| D. |
None of these |
 |
The plane is x + 3y + z – 4 + `lamda`(2x – y) = 0 This is always passes through the intersection of the planes x + 3y + z – 4 = 0 and 2x – y = 0. which is a line.
Now 2x – y = 0
`=> x/1=y/2`
x + 3y +z – 4 = 0
`=>`x + 3.2x + z – 4 = 0
7x +z – 4 = 0
7x = –(z – 4)
`=>x/1=(z-4)/-7`
Therefore, the line is `x/1=y/2=(z-4)/-7`