# In Following Cases, Determine the Direction Cosines of the Normal to the Plane and the Distance from the Origin. Z = 2 - Mathematics

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

z = 2

#### Solution

The equation of the plane is z = 2 or 0x + 0y + z = 2 … (1)

The direction ratios of normal are 0, 0, and 1.

:.sqrt(0^2 + 0^2 + 1^2)  = 1

Dividing both sides of equation (1) by 1, we obtain

0.x + 0.y + 1.z = 2

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

Therefore, the direction cosines are 0, 0, and 1 and the distance of the plane from the origin is 2 units.

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#### APPEARS IN

NCERT Class 12 Maths
Chapter 11 Three Dimensional Geometry
Q 1 | Page 493