Finding volume of pyramid in R 3 .Assume we have a pyramid (triangular base) sitting in R 3 , i.e. we have the coordinates for the vertices A,B,C and D. How can we find the volume of the pyramid without using either its height or its base area and no advanced tools like integration?

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Finding volume of pyramid in             R        3  .Assume we have a pyramid (triangular base) sitting in             R        3  , i.e. we have the coordinates for the vertices A,B,C and D. How can we find the volume of the pyramid without using either its height or its base area and no advanced tools like integration?

Zechariah Zavala · Accepted Answer

Explanation:Take the vectors       v    1    =  B  −  A,       v    2    =  C  −  A and       v    3    =  D  −  A. The determinant of the matrix whose lines are       v    1  ,       v    2   and       v    3   gives the volume of the parallelepiped with edges given by these vectors.

We have a pyramid (triangular base) sitting in mathbb{R}^{3}, i.e. we have the coordinates for the vertices A,B,C and D.

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