Q. 165.0( 1 Vote )

# If the line drawn from (4, -1, 2) meets a plane at right angles at the point (-10,5,4), find the equation of the plane.

It means the plane passes through the point B (-10, 5, 4). Therefore the position vector of this point is,

And also given the line segment joining points A(4, -1, 2) and B (-10, 5, 4) and is at right angle to it.

Then

Position vector of - position vector of

We know that vector equation of a plane passing through point and perpendicular/normal to the vector is given by

Substituting the values from eqn(i) and eqn(ii) in the above equation, we get

(by multiplying the two vectors using the formula )

is the vector equation of a required plane.

Let

Then, the above vector equation of the plane becomes,

Now multiplying the two vectors using the formula, we get

This is the Cartesian form of the equation of the required plane.

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
Types of solution on the basis of Raoult's Law44 mins
Ray Optics | Getting the basics46 mins
Understant the concept of Development of pollen grains55 mins
Lets understand the ploidy levels of various structures of a flowering plant53 mins
Nucleophilic Substitution Reaction | Getting the basics39 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