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)