$\mathrm{v\text{'}}=\left[\begin{array}{c}-cos\left(\alpha \right)sin\left(\gamma \right)-sin\left(\alpha \right)sin\left(\beta \right)cos\left(\gamma \right)\\ -sin\left(\alpha \right)sin\left(\gamma \right)+cos\left(\alpha \right)sin\left(\beta \right)cos\left(\gamma \right)\\ -cos\left(\beta \right)cos\left(\gamma \right)\end{array}\right]$