Eduprobe
Question:
The distance of the point (1, 3, 7) from the plane passing through the point (1, 1, 1), having normal perpendicular to both the lines x-1 = y+2 = z and x-2 = y+1 = z+7, is.
20√74
10√83
5√83
10√74
Solution:
n=∣∣∣ijk1−631−1−1∣∣∣=5i+7j+3k
Equation of plane is r.n=n.a
(5i+7j+3k)=(5i+7j+3k).(i−j−k)
r.(5i+7j+3k)=−9
Distance =∣∣∣−9∣∣∣√52+72+32=10√83