Work out scalar triple product instantly with clear inputs, formula shown and shareable results.
The scalar triple product a·(b × c) equals the determinant of the matrix with these vectors as rows. Its absolute value is the volume of the parallelepiped they span, and zero means they are coplanar.
Scalar triple product
a · (b × c) = det[a; b; c], with volume = |a · (b × c)|
b × c = (2, 2, −3), so the triple product is 2 + 4 − 9 = −3 and the volume is 3.
Cyclic rotations leave it unchanged; swapping any two vectors flips the sign but not the volume.