How would I solve an equation involving dot product with cross product of $3$ vectors?
$\vec{a} = [-2, 1] $
$\vec{b} = [0, 1]$
$k_1 = 4$
$k_2 = 20$
The expression to solve is: $\dfrac {(\vec{b} \cdot \vec{b}) }{ k_1 }+ \dfrac {(\vec{b} \cdot \vec{a} \times \vec{b} \times \vec{a}) } {k_2}$
In the above expression
. refers to dot product and x refers to cross product.
The answer should be $\dfrac {13} {20}$
The $\dfrac{(\vec{b} \cdot \vec{b}) }{ k_1}$ is $\dfrac 1 4$
How is $\dfrac{(\vec{b} \cdot \vec{a} \times \vec{b} \times \vec{a}) }{ k_2 } = \dfrac {8} {20}$?
Thanks.