3D Geometry
Three Dimensional Geometry
star_batch_jee_advanced_2025
Grade 12

Question:

Equation of plane containing both lines is:
$x + 5y - 3z = 10$
$x + 6y + 5z = 20$
$x + 6y - 5z = 10$
None of these

Step-by-Step Solution

Key Concept: The equation of a plane containing two lines can be found using the determinant form with direction ratios and a point on the first line.
To find the equation of the plane containing both lines, we use the determinant form $\begin{vmatrix} x-2 & y-2 & z-1 \\ 2 & 3 & 4 \\ 3 & 2 & 3 \end{vmatrix} = 0$. Expanding this determinant gives $(x-3)(1) + (y-2)(12-6) + (z-1)(4-9) = 0$, which simplifies to $x + 6y - 5z = 10$.
Correct Answer: 3

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