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 *l*, *m*, *n* 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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