The coordinates of the foot of the perpendicular drawn from origin to the plane \(2x - 3y + 4z - 6 = 0\) is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\left(\displaystyle\frac{12}{29}, -\frac{18}{29}, \frac{24}{29}\right)\)
The perpendicular from the origin runs along the normal of the plane, with direction ratios 2, −3, 4. So the foot is \(N(2t, -3t, 4t)\) for some t.
N lies on the plane:
\(2(2t) - 3(-3t) + 4(4t) - 6 = 0\)
\(29t = 6\)
\( \displaystyle t = \frac{6}{29} \)
Hence
\( \displaystyle N = \left(\frac{12}{29}, -\frac{18}{29}, \frac{24}{29}\right) \)
Note: This topic was not in the CUET 2026 syllabus.