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In Following Cases, Determine the Direction Cosines of the Normal to the Plane and the Distance from the Origin.X + Y + Z = 1 - Mathematics

In following cases, determine the direction cosines of the normal to the plane and the distance from the origin.

x + y + z = 1

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Solution

x + y + z = 1 … (1)

The direction ratios of normal are 1, 1, and 1.

This equation is of the form lx + my + nz = d, where lmn are the direction cosines of normal to the plane and d is the distance of normal from the origin.

Therefore, the direction cosines of the normal are `1/sqrt3, 1/sqrt3 and 1/sqrt3` the distance of normal from the origin is `1/sqrt3` units.

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APPEARS IN

NCERT Class 12 Maths
Chapter 11 Three Dimensional Geometry
Q 1.2 | Page 493
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