Q. 34.2( 34 Votes )

# 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: The vertices of the triangle are P (2a, 2, 6), Q (-4, 3b, -10) and R (8, 14, 2c).

⇒ x_{1} = 2a, y_{1} = 2, z_{1} = 6; x_{2} = -4, y_{2} = 3b, z_{2} = -10; x_{3} = 8, y_{3} = 14, z_{3} = 2c

We know that the coordinates of the centroid of the triangle, whose vertices are (x_{1}, y_{1}, z_{1}), (x_{2}, y_{2}, z_{2}) and (x_{3}, y_{3}, z_{3}), are .

So, the coordinates of the centroid of the triangle PQR are

Now, it is given that the origin (0, 0, 0) is the centroid.

So, we have

⇒ 2a +4 = 0, 3b + 16 = 0, 2c – 4 = 0

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