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Question: If centroid of tetrahedron OABC, where A, B, C are given by (a, 2, 3), (1, b, 2) and (2, 1, c) respe...

If centroid of tetrahedron OABC, where A, B, C are given by (a, 2, 3), (1, b, 2) and (2, 1, c) respectively be (1, 2, –1), then distance of P(a, b, c) from origin is equal to

A

107\sqrt { 107 }

B

14\sqrt { 14 }

C

107/14\sqrt { 107 / 14 }

D

None of these

Answer

107\sqrt { 107 }

Explanation

Solution

(1, 2, –1) is the centroid of the tetrahedron

∴ 1=0+a+1+241 = \frac { 0 + a + 1 + 2 } { 4 }

⇒ a = 1, 2=0+2+b+142 = \frac { 0 + 2 + b + 1 } { 4 }

⇒ b = 5, −1=0+3+2+c4- 1 = \frac { 0 + 3 + 2 + c } { 4 }

⇒ c = – 9.

∴ (a, b, c) = (1, 5, –9).

Its distance from origin=1+25+81=107= \sqrt { 1 + 25 + 81 } = \sqrt { 107 }