an equation of a plane parallel to the plane X - 2y + 2x - 5 = 0 and at a unit distance from the origin is?
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Given :
A plane P:x -2y + 2z - 5 =0
To find :
The equation of a plane parallel to given plane P and at planes a distance of 1 unit from origin. Equation of family of parallel to the given plane P is
=> Q : x - 2y + 2z + d = 0
Also, perpendicular distance of Q from origin is 1 unit.
=> |0 - 2(0)+2(0) + d/√1² + 2² + 2²| =
=> |d/3| = 1
=> d = ±3
=> Hence, the required equation of the plane parallel to P and at unit distance from origin is x - 2y + 2z ± 3 = 0.
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