Answer :

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


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