JEE Mains · Maths · STD 12 - 11. three dimension geometry
The equation of the plane containing the line \(2x- 5y+ z = 3; x +y+ 4z = 5,\) and parallel to the plane, \(x + 3y+ 6z = 1,\) is:
- A \(2x + 6y + 12z = - 13\)
- B \(2x + 6y + 12z = 13\)
- C \(x + 3y + 6z = - 7\)
- D \(x + 3y + 6z = 7\)
Answer & Solution
Correct Answer
(D) \(x + 3y + 6z = 7\)
Step-by-step Solution
Detailed explanation
Let equation of plane containing the lines \(2 x-5 y+z =3 \text { and } x+y+4 z=5 \text { be }\) \((2 x-5 y+z-3)+\lambda(x+y+4 z-5) =0\) \(\Rightarrow(2+\lambda) x+(\lambda -5) y+(4 \lambda+1) z-3-5 \lambda=0 \ldots(i)\) This plane is parallel to the plane \(x+3 y+6 z=1\).…
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