Scalar Triple Product Calculator
Calculate the scalar triple product a · (b × c), parallelepiped volume, and test for coplanarity.
Three Vectors
Vector a
Vector b
Vector c
Presets:
Scalar Triple Product a · (b × c)
1.000000
Parallelepiped Volume
1.000000
|a · (b × c)| = absolute value of scalar triple product
Orientation
right-handed
Positive: a, b, c form right-handed system
b × c (intermediate)
(1.0000, 0.0000, 0.0000)
Cyclic Property Verification
a · (b × c) = 1.000000
b · (c × a) = 1.000000
c · (a × b) = 1.000000
Scalar Triple Product Properties
Determinant Form
a · (b × c) = det([a; b; c])
Equal to the 3×3 determinant with a, b, c as rows
Cyclic Property
a · (b × c) = b · (c × a) = c · (a × b)