If the distance between the points (a, 2, 1) and (1, –1, 1) is 5, then a _______.

Question

Fill in the blanks:

If the distance between the points (a, 2, 1) and (1, –1, 1) is 5, then a _______.

Answer 1

a = -3 or a = 5

Explanation:

Let P be the point whose coordinate is (a, 2, 1) and Q represents the point (1, -1, 1).

Given, PQ = 5

From distance formula-

Squaring both sides-

a² -2a + 10 = 25

⇒ a² -2a - 15 = 0

⇒ a² -5a + 3a - 15 = 0

⇒ a(a-5) + 3(a-5) = 0

⇒ (a + 3)(a – 5) = 0

∴ a = -3 or a = 5