# In Following Cases, Determine the Direction Cosines of the Normal to the Plane and the Distance from the Origin. 5y + 8 = 0 - Mathematics

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

5y + 8 = 0

#### Solution

5y + 8 = 0

⇒ 0x − 5y + 0z = 8 … (1)

The direction ratios of normal are 0, −5, and 0.

:. sqrt(0+(-5)^2 + 0) = 5

Dividing both sides of equation (1) by 5, we obtain

-y = 8/5

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 to the plane are 0, −1, and 0 and the distance of normal from the origin is 8/5 units.

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#### APPEARS IN

NCERT Class 12 Maths
Chapter 11 Three Dimensional Geometry
Q 1.4 | Page 493