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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 `vecr`is 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.
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