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.
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