Question

Show that the line segment joining the points A (1, 2, 3) and B (4, 5, 7) is parallel to the line segment joining the points C (-4, 3, -6) and D (2, 9, 2).

Answer 1

Line joining A (1, 2, 3) and B (4, 5, 7) is written as

AB = 3i + 3j + 4k

Line joining C (-4, 3, -6) and D (2, 9, 2) is written as

CD = 6i + 6j + 8k

Here if CD = r (AB) where r is a scalar constant

So the two lines are parallel CD = 2 AB

Hence, the two lines are parallel.