FIND THE COORDINATES OF THE FOOT OF THE PERPENDICULAR AND THE PERPENDICULAR DISTANCE OF THE POINT P(3,2,1) FROM THE PLANE 2X-Y+Z+1=0. FIND ALSO, THE IMAGE OF THE POINT IN THE PLANE
Asked by | 6th Feb, 2011, 12:00: AM
we know that the distance of a point from the plane Ax+By+Cz+d=0
here the point is (3,2,1) and plane is 2X-Y+Z+1=0
now put these values in the formula and get the answer.
By the reflection of a point in a plane we mean that,
a point which is at the same distance from the plane but on the other side of the plane and the line joining a point and its reflection is perpendicular to the plane.
normal to the given plane is along the direction (2,-1,1)
so the reflection lies along the line
let for some k, it represents the foot of the perpendicular from the given point to the given plane.
solving we get the value of k
put this value in x,y and z found above to get the reflection.
Answered by | 5th Mar, 2011, 09:11: PM
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