Q. 8

Find the equations of planes parallel to the plane x – 2y + 2z = 3 which are at a unit distance from the point (1, 2, 3).

Answer :

Formula : Plane = r . (n) = d


Where r = any random point


n = normal vector of plane


d = distance of plane from origin


If two planes are parallel , then their normal vectors are same


Therefore ,


Parallel Plane x – 2y + 2z – 3 = 0


Normal vector = (i - 2j + 2k)


Normal vector of required plane = (i - 2j + 2k)


Equation of required planes r . (i - 2j + 2k) = d


In cartesian form x – 2y + 2y = d


It should be at unit distance from point (1,2,3)


Distance






For + sign = > 3 = 3 - d = > d = 0


For - sign = > 3 = - 3 + d = > d = 6


Therefore equations of planes are : -


For d = 0 For d = 6


x – 2y + 2y = d x – 2y + 2y = d


x – 2y + 2y = 0 x – 2y + 2y = 6


Required planes = x – 2y + 2y = 0


x – 2y + 2y – 6 = 0


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
The Embryonic DevelopmentThe Embryonic DevelopmentThe Embryonic Development62 mins
NCERT Exemplar Special | The Living World Part 2NCERT Exemplar Special | The Living World Part 2NCERT Exemplar Special | The Living World Part 225 mins
Nernst Equation - Learn the ConceptNernst Equation - Learn the ConceptNernst Equation - Learn the Concept33 mins
Revising the basics of Organic ChemistryRevising the basics of Organic ChemistryRevising the basics of Organic Chemistry35 mins
Understanding the Combination of cellsUnderstanding the Combination of cellsUnderstanding the Combination of cells54 mins
Types of solution on the basis of Raoult's LawTypes of solution on the basis of Raoult's LawTypes of solution on the basis of Raoult's Law44 mins
Nucleophilic Substitution Reaction | Getting the basicsNucleophilic Substitution Reaction | Getting the basicsNucleophilic Substitution Reaction | Getting the basics39 mins
Lets understand the ploidy levels of various structures of a flowering plantLets understand the ploidy levels of various structures of a flowering plantLets understand the ploidy levels of various structures of a flowering plant53 mins
Know About finding the Adjoint & Inverse Of MatrixKnow About finding the Adjoint & Inverse Of MatrixKnow About finding the Adjoint & Inverse Of Matrix46 mins
Getting into the world of coliisionsGetting into the world of coliisionsGetting into the world of coliisionsFREE Class
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses