Scalar triple product
Scalar triple product is an interactive experiment in Vectors, a free simulation from StudyFi Lab that runs right in your browser.
The scalar triple product (a × b)·c is a number equal to the determinant of the components of a, b and c. Its absolute value is the volume of the parallelepiped the three vectors span. When it is zero, the parallelepiped is flat: all three vectors lie in one plane (they are coplanar).
Try this: Set c = a − b, which is c = (3, −1, −1) for the starting a and b: the volume drops to zero. Then raise c₃ and watch the solid puff up.
Frequently asked questions
What does the “Scalar triple product” experiment show?
The scalar triple product (a × b)·c is a number equal to the determinant of the components of a, b and c. Its absolute value is the volume of the parallelepiped the three vectors span. When it is zero, the parallelepiped is flat: all three vectors lie in one plane (they are coplanar).
How do I try “Scalar triple product”?
Set c = a − b, which is c = (3, −1, −1) for the starting a and b: the volume drops to zero. Then raise c₃ and watch the solid puff up.
Studying for a test?
Upload your notes and StudyFi turns them into flashcards, tests and podcasts.