Euclidean spaces

Choose such values of $b$, that the following relation

$$\left\lang\begin{pmatrix}x_{1}\\y_{1}\\z_{1}\end{pmatrix},\begin{pmatrix}x_{2}\\ y_{2}\\ z_{2}\end{pmatrix}\right\rang = 3x_{1}x_{2} - b(x_{1}y_{2} + x_{2}y_{1}) + 4y_{2}y_{1} + z_{1}z_{2}$$defines an inner product on $\mathbb{R}^{3}$ correctly.