Q. 205.0( 1 Vote )

# Write the vector equation of the plane, passing through the point (a, b, c) and parallel to the plane .

The required plane is parallel to , so required plane and the given plane must have the same normal vector.

Vector normal to the plane is The required plane is passing through a given point

(a, b, c), so can write the position vector of the point as Now, the equation of the required plane is given by,    (x - a) + (y - b) + (z - c)=0

x + y + z - (a + b + c)=0

x + y + z = a + b + c

Hence, the equation of the plane passing through (a, b, c) and parallel to the plane is i.e. (in vector form), or, in general form x + y + z = a + b + c.

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 Development62 mins  NCERT Exemplar Special | The Living World Part 225 mins  Nernst Equation - Learn the Concept33 mins  Revising the basics of Organic Chemistry35 mins  Understanding the Combination of cells54 mins  Nucleophilic Substitution Reaction | Getting the basics39 mins  Types of solution on the basis of Raoult's Law44 mins  Understant the concept of Development of pollen grains55 mins  Getting into the world of coliisionsFREE Class  Know About finding the Adjoint & Inverse Of Matrix46 mins
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 view all courses RELATED QUESTIONS :

Find the coordinate of the point P where the line through and crosses the plane passing through three points and Also, find the ratio in which P divides the line segment AB.

Mathematics - Board Papers