Question

If two of the vertices of the triangle are A(3, 1, 4) and B(-4, 5, -3) and the centroid of a triangle is G(-1, 2, 1), then find the coordinates of the third vertex C of the triangle.

Answer 1

 Let \(\overline{a},\overline{b},\overline{c}\) and \(\overline{g}\) be the position vectors of A, B, C and G respectively.

Since G is the centroid of the ∆ABC, by the centroid formula,

∴ the coordinates of third vertex C are (-2, 0, 2).