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  • An equation of a plane parallel to the plane x – 2y + 2z – 5 = 0 and at a unit distance from the origin isOption: 1 x – 2y + 2z &nd

An equation of a plane parallel to the plane x – 2y + 2z – 5 = 0 and at a unit distance from the origin is

Option: 1

x – 2y + 2z – 3 = 0


Option: 2

x – 2y + 2z + 1 = 0


Option: 3

x – 2y + 2z – 1 = 0


Option: 4

x – 2y + 2z + 5 = 0


Answers (1)

best_answer

 

 

Family of Plane -

Equation of plane parallel to a given plane

Parallel planes have the same normal vectors, so the equation of plane parallel to \vec {\mathbf r}\cdot \vec {\mathbf n}=d_1 is of the form \vec {\mathbf r}\cdot \vec {\mathbf n}=d_2, where d2 can be determined by using the given conditions.

 

In cartesian form, if ax + by +cz + d = 0 is given plane, then  the plane parallel to this plane is ax + by + cz + k = 0, where d and k is any scalar.

 

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:    Equation of a plane parallel to

x-2y +2z-5= 0

and at a unit distance from origin is x-2y +2z+k= 0

\Rightarrow \frac{\left | k \right |}{3}= 1\Rightarrow \left | k \right |= 3

\therefore x-2y+2z-3=0

or\: \: x-2y+2z+3=0

Posted by

Pankaj Sanodiya

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