Let P be the point of intersection of the line 
and the plane x + y + z = 2. If the distance of the point P from the plane 3z – 4y + 12z = 32 is q, then q and 2q are the roots of the equation
Text Solution
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Given.
P be the point of intersection of the line 
and the plane x + y + z = 2
Now let, 
Say. point A(3 
- 3, 
- 2, 1 - 2 
)
Since point lie on the plane also.
So, 3 
- 3 + 
- 2 + 1 - 2 
= 2
2 
=6
= 3
Hence, the point will be P(6, 1, - 5)
Now finding the distance of the point P(6, 1, - 5) from the plane 3x – 4y + 12z = 32 we get.
Equation with roots q and 2q will be.
x 2 – 3qx + 2q 2 = = 0
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