First slide

Introduction to 3-D Geometry

Question

Origin is the centroid of the triangle formed by $(a, 1, 3)$ , $(- 2, b, - 5)$ and $(4, 7, c)$ then ascending order of $a, b, c$ is.

Easy

A

$b, a, c$
B

$a, b, c$
C

$b, c, a$
D

$c, a, b$

Solution

The centroid of the triangle formed by the points $A (x_{1}, y_{1}, z_{1}), B (x_{2}, y_{2}, z_{2}), C (x_{3}, y_{3}, z_{3})$ is $G (\frac{x_{1} + x_{2} + x_{3}}{3}, \frac{y_{1} + y_{2} + y_{3}}{3}, \frac{z_{1} + z_{2} + z_{3}}{3})$
It implies that $(\frac{a - 2 + 4}{3}, \frac{1 + b + 7}{3}, \frac{3 - 5 + c}{3}) = (0, 0, 0)$
Hence, $a = - 2, b = - 8, c = 2$
The ascending order of the values of $a, b, c$ is $b, a, c$

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