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.

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Solution

It is known that the coordinates of the centroid of the triangle, whose vertices are (x₁, y₁, z₁), (x₂, y₂, z₂) and (x₃, y₃, z₃), are.

Therefore, coordinates of the centroid of ΔPQR

It is given that origin is the centroid of ΔPQR.

Thus, the respective values of a, b, and c are

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If the origin is the centriod of the triangle PQR with vertices $P (2 a, 2, 6), Q (- 4, 3 b, - 10)$ and $R (8, 14, 2 c),$ then find the values of a, b, and c.

If the origin is the centroid of the triangle with vertices P(2a, 2, 6), Q(-4, 3b, -10) and R(8, 14, 2c), find the values of a,b and c. Also, determine the value of $a^{2} + b^{2} - c^{2}$ .

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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.

It is known that the coordinates of the centroid of the triangle, whose vertices are (x1, y1, z1), (x2, y2, z2) and (x3, y3, z3), are. Therefore, coordinates of the centroid of ΔPQR It is given that origin is the centroid of ΔPQR. Thus, the respective values of a, b, and c are