Engineering
Mathematics
Plane and Its Different Forms
Distance from a Plane
Question
The foot of the perpendicular from the point A(7,14,5) to the plane 2x + 4y − z = 2 is?
Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.
Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA
Solution
Let N be the foot of the perpendicular drawn from the point A(7,14,5) and perpendicular to the plane 2x + 4y − z = 2
Then, the equation of the line PN is (say)
Let the coordinates of N be N(2λ + 7,4λ + 14, −λ + 5)
Since N lies on the plane 2x + 4y − z = 2, so
2(2λ + 7) + 4(4λ + 14) − (−λ + 5) = 2
⇒ 21λ = −63
⇒λ = −3
∴ required foot of the perpendicular is
N(−6 + 7, −12 + 14, 3 + 5), i.e., N(1,2,8).