vault backup: 2026-06-10 10:57:11

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@@ -37,7 +37,7 @@ Used to project vector $v$ onto $u$
![[VectorProjection.excalidraw]]
### Triple Scalar Product
Find the Determinant of:
$$u * (v \times w) = \begin{vmatrix} u_{1} && u_{2} && u_{3} \\ u_{1} && u_{2} && u_{3} \\ u_{1} && u_{2} && u_{3} \end{vmatrix}$$
$$u * (v \times w) = \begin{vmatrix} u_{1} && u_{2} && u_{3} \\ v_{1} && v_{2} && v_{3} \\ w_{1} && w_{2} && w_{3} \end{vmatrix}$$
The triple scalar product can also be found by finding the cross product of $v$ and $w$ and then taking the dot product of the resulting vector and $u$.
$$u * (v \times w) = (u \times v) * w $$
The triple scalar product is equal to the volume of the parallelpiped where each vector represents one adjacent edge.