Question

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

Answer 1

Let AB be the lines joining the points (1,-1,2) and (3,4,-2), and CD be the lines joining the points, (0,3,2), (3,5,6).

The direction ratios: a1,b1,c1 of AB are (3-1), (4-(-1)), and (-2-2) i.e., 2, 5, and -4.
The direction ratios: a2,b2,c2 of CD are (3-0), (5-3), and (6-2) i.e., 3, 2, and 4.
AB and CD will be perpendicular to each other if a1a2+b1b2+c1c2=0

a1a2+b1b2+c1c2
=2×3+5×2+(-4)×4
=6+10-16
=0

Therefore, AB and CD are perpendicular to each other.