AP EAMCET · Maths · Three Dimensional Geometry
If origin is the centroid of the triangle \(P Q R\) with vertices \(P(2 a, 2,6), Q(-4,3 b,-10)\) and \(R(8,14,2 c)\), then the values of \(a, b, c\) respectively are
- A \(2, \frac{16}{3},-2\)
- B \(-2,-\frac{16}{3},-2\)
- C \(-2,-\frac{16}{3}, 2\)
- D \(-2, \frac{16}{3},-2\)
Answer & Solution
Correct Answer
(C) \(-2,-\frac{16}{3}, 2\)
Step-by-step Solution
Detailed explanation
Centroid is given by, \(\begin{aligned} & x=\frac{x_1+x_2+x_3}{3} \\ & y=\frac{y_1+y_2+y_3}{3} \\ & z=\frac{z_1+z_2+z_3}{3} \end{aligned}\) Using values given, \(0=\frac{2 a-4+8}{3} \Rightarrow a=-2\) Also, \(\quad 0=\frac{2+3 b+14}{3}, b=\frac{-16}{3}\) and…
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