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Wiki/Math/Vector Basics.md

@@ -15,4 +15,10 @@ Properties:
 - Anti-commutative $$ u \times v = -(v \times u) $$
 - On self $$ a \times a = 0 $$
 The magnitude of the cross product of two vectors can be found with $$||u \times v|| = ||u|| * ||v|| * \sin(\theta)$$
-The magnitude of the cross product is equal to the 
+The magnitude of the cross product is equal to the area of the parallelogram formed with two adjacent sides as the vectors.
+### Triple Scalar Product
+Find the Determinant of:
+$$u * (v \times w) = \begin{vmatrix} u_{1} && u_{2} && u_{3} \\ u_{1} && u_{2} && u_{3} \\ u_{1} && u_{2} && u_{3} \end{vmatrix}$$
+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.