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).
Answer :
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 :
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
Write the direction cosines of a line equally inclined to the three coordinate axes.
Mathematics - Board PapersFind the angle between the following pair of lines:
and
and check whether the lines are parallel or perpendicular.
Mathematics - Board PapersFind the coordinates of the foot of perpendicular, and the perpendicular distance from the point P(4, 3, 2) to the plane 
Also find the image of P in the plane.
Find a vector 
of magnitude 5√2, making an angle of 
with x-axis., 
with y-axis and an acute angle θ with z-axis.
If a line makes angles 90°, 60° and θ with x, y and z-axis respectively, where θ is acute, then find θ.
Mathematics - Board Papers