Q. 3

# Show that the line joining the points A(1,-1, 2) and B(3, 4, -2) is perpendicular to the line joining the points C(0, 3, 2) and D (3, 5, 6).

Given: A(1, -1, 2) and B(3, 4, -2)

The line joining these two points is given by,

AB = 2i + 5j -4k

C(0, 3, 2) and D(3, 5, 6),

The line joining these two points,

CD = 3i + 2j +4k

To prove that the two lines are perpendicular we need to show that the angle between these two lines is

So, AB.CD = 0 (dot product)

Thus, (2i + 5j -4k). (3i + 2j +4k) = 6 + 10 – 16 = 0.

Thus, the two lines are perpendicular.

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
Questions Based on 3D Geometry | Check Yourself40 mins
Important concepts of Metallurgy7 mins
Application of Biotechnology | Concepts - 0256 mins
Fundamental Integration Formula59 mins
Application of Biotechnology | Concepts - 0160 mins
Complete revision of amines| Concepts at fingertips43 mins
Carbocation | Mastering important concepts64 mins
Revision of straight lines important formulas in one shot59 mins
Concept Builder Questions of straight Lines (Quiz Session)55 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