Question

two vertices of a traingle are A(2,-4,3) and B (3,-1,-2) and its centroid is G(1,0,3) .The third vertex C is

Answer 1

HELLO FRIEND HERE IS YOUR ANSWER,,,,,

Given,,,

A => ( 2i , - 4j , 3k) , B => (3i , - j , - 2k) ,
G => (i, 0j , 3k)

Let The unknown number or value be variable "x".

C => (xi , xj , xk)

We know that,,,

The centroid G formula will be,,

$g = \frac{a + b + c}{3}$

Therefore,,,,,,

$3(i + 3k) = (2i - 4j + 3k) + (3i - j - 2k) + (xi + xj + xk) \\ \\ \\ 3i + 9k = ((2i + 3i) + ( - 4j - j) + (3k - 2k) \\ \\ \\ 3i + 9k = (5i - 5j + k) + (xi + xj + xk)$

By simplifying the given method to find values of "C" vertex.

$(5i - 5j + k) - (3i + 9k) = (xi + xj + xk) \\ \\ \\ so \: \: \: the \: \: \: \: answer \: \: \: becomes \\ \\ \\ c \: = \: (2i - 5j - 8k)$

HOPE IT HELPS YOU AND SOLVES YOUR DOUBTS ABOUT FINDING OTHER VERTEXES BY USING CENTROID "G" FORMULA!!!!!