Q. 195.0( 2 Votes )

# If the lines and are perpendicular, find the value of k and hence find the equation of the plane containing these lines.

The direction ratio of the line is r1 = (– 3, – 2k, 2)

The direction ratio of the line is r2 = (k, 1, 5)

Since the line and are perpendicular so

r1.r2 = 0

(– 3, – 2k, 2). (k, 1, 5) = 0

– 3k – 2k + 10 = 0

– 5k = – 10

k = 2

the equation of the line are and

The equation of the plane containing the perpendicular lines and is

(– 20 – 2)x – y(– 15 – 4) + z(– 3 + 8) = d

– 22x + 19y + 5z = d

The line pass through the point (1, 2, 3) so putting x = 1, y = 2, z = 3 in the equation – 22x + 19y + 5z = d we get

– 22(1) + 19(2) + 5(3) = d

d = – 22 + 38 + 15

d = 31

The equation of the plane containing the lines is – 22x + 19y + 5z = 31

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Questions Based on 3D Geometry26 mins
Revision of straight lines important formulas in one shot59 mins
Concept Builder Questions of straight Lines (Quiz Session)55 mins
Reminding 11th - Revision of Circles important formulas in 50 Minutes56 mins
Conic Section Part 164 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