Finding the volume of the tetrahedron.Find the volume of the tetrahedron with the vertices P(1,1,1), Q(1,2,3), R(3,1,2), and S(2,3,1).

Question

Jaelyn Rosario · Accepted Answer

Step 1Volume of a tetrahedron is             1      3        ×  Base area  ×  heightStep 2If the vertices are                     v        1            →        ,                    v        2            →        ,                    v        3            →        ,                    v        4            →      , then the volume is given by      |                            (                                                    v                →                                      2                    −                                                    v                →                                      1                    )          ⋅                      (            (                                                            v                  →                                            3                        −                                                            v                  →                                            1                        )            ×            (                                                            v                  →                                            4                        −                                                            v                  →                                            1                        )            )                          6              |  where             a      →        ⋅            b      →       denotes the inner/dot product, and             a      →        ×            b      →       denotes the cross product.

Find the volume of the tetrahedron with the vertices P(1,1,1), Q(1,2,3), R(3,1,2), and S(2,3,1).

Answered question

Answer & Explanation

New Questions in High school geometry