Cartesian equation of plane passing through the points (2, −4, 5) and perpendicular to the line with direction ratios (3, −1, 2) is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(3x-y+2z=20\)
The plane is perpendicular to the line, so the line’s direction ratios (3, −1, 2) are the direction ratios of the normal to the plane.
The plane through \((x_1, y_1, z_1)\) with normal direction ratios a, b, c is \(a(x-x_1)+b(y-y_1)+c(z-z_1)=0\). With the point (2, −4, 5):
\( 3(x-2)-1(y+4)+2(z-5)=0 \)
\( 3x-6-y-4+2z-10=0 \)
\( 3x-y+2z=20 \)
Check: \(3(2)-(-4)+2(5)=6+4+10=20\).
Note: This topic was not in the CUET 2026 syllabus.