Show that the line through the points (1,1,−2),(3,4,−2) is perpendicular to the line through the points (0,3,2) and (3,5,6).

Engineering

Mathematics

Vector Product of Two Vectors

Equation of Straight Line in 3D

Question

Show that the line through the points (1,1,−2),(3,4,−2) is perpendicular to the line through the points (0,3,2) and (3,5,6).

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Let A(1,−1,2),B(3,4,−3),C(0,3,2),D(3,5,6)

Dr′ of AB = (2,5,−4)

Dr′ of CD = (3,2,4)

a₁a₂+ b₁b₂+ C₁C₂= 2 × 3 + 5 × 2 + −4 × 4 = 0

Hence the lines are perpendicular.