The co-ordinates of the foot of the perpendicular drawn from the origin to the plane \(5x+2y+2z=1\) are:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\left(\displaystyle\frac{5}{33},\frac{2}{33},\frac{2}{33}\right)\)
The perpendicular from the origin runs along the normal (5, 2, 2), so the foot is
\(N = (5t, 2t, 2t)\) for some t.
N lies on the plane:
\(5(5t)+2(2t)+2(2t) = 1\)
\(33t = 1\)
\( \displaystyle t = \frac{1}{33} \)
Hence the foot of the perpendicular is
\( \displaystyle \left(\frac{5}{33},\frac{2}{33},\frac{2}{33}\right) \)
Note: This topic was not in the CUET 2026 syllabus.