Given: distance between the points P(a, 2, 1) and Q(1, -1, 1) is 5 units

To find: the value of a

Formula used:

The distance between any two points (a, b, c) and (m, n, o) is given by,

PQ = 5 units

The distance between points P(a, 2, 1) and Q(1, -1, 1) is PQ

Squaring both sides:

⇒ a² – 2a + 10 = 25

⇒ a² – 2a + 10 – 25 = 0

⇒ a² – 2a – 15 = 0

⇒ a² – 5a + 3a – 15 = 0

⇒ a(a – 5) + 3(a – 5) = 0

⇒ (a – 5) (a + 3) = 0

⇒ a = 5 or -3

Hence, the value of a is 5 or -3