Question:
If the origin is the centroid of the triangle PQR with vertices P (2a, 2, 6), Q (- 4, 3b, -10) and R(8, 14, 2c), then find the values of a, b and c.
Answer:
Given Centroid of triangle = (0,0,0)
=> {(2a - 4 + 8)/3 , (2+ 3b + 14)/3, (6 - 10 + 2c)/3} = (0,0,0)
=> {(2a - 4)/3 , (3b + 16)/3, (2c - 4)/3} = (0,0,0)
Now (2a - 4)/3 = 0
=> 2a - 4 = 0
=> 2a = 4
=> a = 4/2
=> a = 2
Agian
(3b + 16)/3 = 0
=> 3b + 16 = 0
=> 3b = -16
=> b = -16/3
And
(2c - 4)/3 = 0
=> 2c - 4 = 0
=> 2c = 4
=> c = 4/2
=> c = 2
So a = 2, B = -16/3 and c = 2
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