CUET · MATHS · PYQ PAPER 2023
The equation of a plane passing through the points \((1,2,3),(4,2,3)\) and \((-1,0,6)\) is given by:
- A \(3 y-2 z+12=0\)
- B \(9 y+18-6 z=0\)
- C \(3 y+2 z+12=0\)
- D \(-3 y-2 z+12=0\)
Answer & Solution
Correct Answer
(D) \(-3 y-2 z+12=0\)
Step-by-step Solution
Detailed explanation
\(\vec{u} = (4-1, 2-2, 3-3) = (3, 0, 0)\) \(\vec{v} = (-1-1, 0-2, 6-3) = (-2, -2, 3)\) \(\vec{n} = \vec{u} \times \vec{v} = (0 \cdot 3 - 0 \cdot (-2), 0 \cdot (-2) - 3 \cdot 3, 3 \cdot (-2) - 0 \cdot (-2)) = (0, -9, -6)\) \(0(x-1) - 9(y-2) - 6(z-3) = 0\)…
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