Question

Show that the points A(1, 2, 7), B(2, 6, 3) and C(3, 10, –1) are collinear.

Answer 1

The given points are A(1, 2, 7), B (2, 6, 3) and C(3, 10, −1).

vector AB = (2i + 6j + 3k) - (i + 2j + 7k) = i + 4j - 4k

⇒ | vector AB| = √(1 + 16 + 16)  = √33

vector BC = (3i + 10j - k) - (2i +6j + 3k) = i + 4j - 4k

⇒ |vector BC| = √(1 + 16 + 16) = √33

and vector AC = (3i + 10j - k) - (i + 2j + 7k) = 2i + 8j - 8k

⇒|vector AC| = √(4 + 64 + 64) = √132 = 2√33

|vector AC| = |vector  AB| + |vector BC|

Hence, the given points A, B and C are collinear.