We will work with geometric problems using spatial vectors.
Example ① For the four points A(1,0,0), B(0,1,0), C(0,0,1), and D(1,1,1), find the centroid G of tetrahedron ABCD.
Solution:G = ((1+0+0+1)/4, (0+1+0+1)/4, (0+0+1+1)/4) = (1/2, 1/2, 1/2)
Solution:G = ((1+0+0+1)/4, (0+1+0+1)/4, (0+0+1+1)/4) = (1/2, 1/2, 1/2)
Key Point
- The centroid of a tetrahedron is the average of its four vertices.
Practice Problems
- Find the centroid of triangle ABC for A(2,0,0), B(0,3,0), and C(0,0,4).
Solution and Explanation
- Answer:(2/3, 1, 4/3)