Question -
Answer -
Given:
The points (1, –1, 2),(3, 4, –2) and (0, 3, 2), (3, 5, 6).
Let us consider AB bethe line joining the points, (1, -1, 2) and (3, 4, -2), and CD be the linethrough the points (0, 3, 2) and (3, 5, 6).
Now,
The direction ratios,a1, b1, c1 of AB are
(3 – 1), (4 – (-1)),(-2 – 2) = 2, 5, -4.
Similarly,
The direction ratios,a2, b2, c2 of CD are
(3 – 0), (5 – 3), (6 –2) = 3, 2, 4.
Then, AB and CD willbe perpendicular to each other, if a1a2 + b1b2 +c1c2 = 0
a1a2 +b1b2 + c1c2 = 2(3) + 5(2)+ 4(-4)
= 6 + 10 – 16
= 0
∴ AB and CD areperpendicular to each other.