Question -
Answer -
Given:
The points (4, 7, 8),(2, 3, 4) and (–1, –2, 1), (1, 2, 5).
Let us consider AB bethe line joining the points, (4, 7, 8), (2, 3, 4) and CD be the line through thepoints (–1, –2, 1), (1, 2, 5).
Now,
The direction ratios,a1, b1, c1 of AB are
(2 – 4), (3 – 7), (4 –8) = -2, -4, -4.
The direction ratios,a2, b2, c2 of CD are
(1 – (-1)), (2 –(-2)), (5 – 1) = 2, 4, 4.
Then AB will beparallel to CD, if
So, a1/a2 =-2/2 = -1
b1/b2 =-4/4 = -1
c1/c2 =-4/4 = -1
∴ We can say that,
-1 = -1 = -1
Hence, AB is parallelto CD where the line through the points (4, 7, 8), (2, 3, 4) is parallel to theline through the points (–1, –2, 1), (1, 2, 5)