SUMMARY
The correct method to calculate the volume of a tetrahedron formed by points P1(2,-1,4), P2(-1,0,3), P3(4,3,1), and P4(3,-5,0) involves using the formula V = (1/6) * |A · (B × C)|, where A, B, and C are vectors derived from the points. The vectors were correctly identified as A = P1P2, B = P1P3, and C = P1P4. However, the calculated triple scalar product was incorrectly computed as 29; the correct value is 101, leading to the volume V = 101/6.
PREREQUISITES
- Understanding of vector operations, specifically cross product and dot product.
- Familiarity with determinants and their application in calculating volumes.
- Knowledge of 3D coordinate geometry and vector representation.
- Basic algebra for manipulating equations and fractions.
NEXT STEPS
- Study how to compute the cross product of vectors in three-dimensional space.
- Learn about determinants and their role in vector calculus.
- Explore the geometric interpretation of the triple scalar product.
- Practice calculating volumes of other polyhedra using similar methods.
USEFUL FOR
Students studying geometry, mathematics educators, and anyone interested in computational geometry or vector calculus.