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A variable plane lx+my+nz = p (where l, m, n are direction cosines of normal) axes at points A, B and C, respectively. Show that the foot of the normal on the pl orthocentre of triangle ABC and hence find the coordinates of the circumcentre of

A variable plane lx+my+nz = p (where l, m, n are direction cosines of normal) axes at points A, B and C, respectively. Show that the foot of the normal on the pl orthocentre of triangle ABC and hence find the coordinates of the circumcentre of

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A variable plane lx +my+nz = p (where l, m, n are direction cosines of normal) intersects the coordinate axes at points A, B and C, respectively. Show that the foot of the normal on the plane from the origin is the orthocentre of triangle ABC and hence find the coordinates of the circumcentre of triangle ABC.
Transcribed Image Text:A variable plane lx +my+nz = p (where l, m, n are direction cosines of normal) intersects the coordinate axes at points A, B and C, respectively. Show that the foot of the normal on the plane from the origin is the orthocentre of triangle ABC and hence find the coordinates of the circumcentre of triangle ABC.
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