Vector Triple Product

#Math

$\displaystyle \vec{a}\times(\vec{b}\times \vec{c})=\vec{b}(\vec{a}\cdot \vec{c})-\vec{c}(\vec{a}\cdot \vec{b})$

Mnemonic

• BAC-CAB
• First vector in parenthesis scaled by dot product of other two vectors - second vector in parenthesis scales by a dot product of other two vectors
  • i.e. The value of a triple vector product is a linear combination of two vectors in the parenthesis; the coefficient of each vector is the dot product of the other two; the middle vector in the triple product always has the positive sign