Q. 12

# Write the value of k for which the planes 2x – 5y + kz = 4 and x + 2y – z = 6 are perpendicular to each other.

Given : equations of perpendicular planes-

2x – 5y + kz = 4

x + 2y – z = 6

To Find : k

Formulae :

Normal vector to the plane :

If equation of the plane is ax + by + cz = d then,

Vector normal to the plane is given by, For given planes –

2x – 5y + kz = 4

x + 2y – z = 6

normal vectors are  As given vectors are perpendicular, hence their normal vectors are also perpendicular to each other.  (2×1) + (-5×2) + (k×(-1)) = 0

2 – 10 – k = 0

- 8 – k = 0

k = -8

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  Understanding the Combination of cells54 mins  Revising the basics of Organic Chemistry35 mins  Nucleophilic Substitution Reaction | Getting the basics39 mins  Types of solution on the basis of Raoult's Law44 mins  Know About finding the Adjoint & Inverse Of Matrix46 mins  Understant the concept of Development of pollen grains55 mins  Getting 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 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