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.


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