Question

The foot of the perpendicular drawnfrom the origin to the plane x+y+z=3 is

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Answer 1

Explanation

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Perpendicular distance of a plane ax + by + cz +

Let A(x, y, z) be the foot of the perpendicular drawn from the origin to the plane x + y + z = 3.

As we know that, the perpendicular distance of a plane ax + by + cz + d = 0 from a point P (x1, y1, z1) is given by:

So, the distance between the origin and the plane x + y + z - 3 = 0 is given by:

So, this means that the length of the line joining the points origin and A is √3

if A = (1, 1, 1) then the distance between the points origin and A is √3