Show that the line segment joining the points A (1, 2, 3) and B (4, 5,

1.	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» 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.

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»

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.