# Find the Cartesian Equation of the Following Planes: Vecr.(Hati + Hatj-hatk) = 2 - Mathematics

#### Question

Find the Cartesian equation of the following planes:

vecr.(hati + hatj-hatk) = 2

#### Solution

It is given that equation of the plane is

vecr.(hati + hatj-hatk) = 2

For any arbitrary point P (xyz) on the plane, position vector vecris given by,

vecr = xhati +yhatj-zhatk

Substituting the value of vecr in equation (1), we obtain

(xhati + yhatj - zhatk).(hati + hatj - hatk) = 2

=> x + y - z = 2

This is the Cartesian equation of the plane.

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#### APPEARS IN

NCERT Solution for Mathematics Textbook for Class 12 (2018 (Latest))
Chapter 11: Three Dimensional Geometry
| 3.1 | Page no. 493

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Find the Cartesian Equation of the Following Planes: Vecr.(Hati + Hatj-hatk) = 2 Concept: Vector and Cartesian Equation of a Plane.