Show that the points A (2, 3, 4), B (-1, -2, 1) and C (5, 8, 7) are co

1.	Show that the points A (2, 3, 4), B (-1, -2, 1) and C (5, 8, 7) are collinear.
Answer» It is given that A (2, 3, 4), B (-1, -2, 1) and C (5, 8, 7) AB = – 3i – 5j – 3k So the point on the line AB with A on the line R = (2, 3, 4) + a (- 3, -5, -3) Consider C = (2 – 3a, 3 – 5a, 4 – 3a) So we get (5, 8, 7) = (2 – 3a, 3 – 5a, 4 – 3a) Here if a = -1 we get LHS = RHS So the point C lies on the line joining AB Therefore, the three points are collinear.

Show that the points A (2, 3, 4), B (-1, -2, 1) and C (5, 8, 7) are collinear.

Answer»

It is given that

A (2, 3, 4), B (-1, -2, 1) and C (5, 8, 7)

AB = – 3i – 5j – 3k

So the point on the line AB with A on the line

R = (2, 3, 4) + a (- 3, -5, -3)

Consider C = (2 – 3a, 3 – 5a, 4 – 3a)

So we get

(5, 8, 7) = (2 – 3a, 3 – 5a, 4 – 3a)

Here if a = -1 we get LHS = RHS

So the point C lies on the line joining AB

Therefore, the three points are collinear.