If $\mathbf{a}=3 \hat{\mathbf{i}}-\hat{\mathbf{j}}+5 \hat{\mathbf{k}}$ and $\mathbf{b}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}$ are given vector. A vector $\mathbf{c}$ which is perpendicular to $Z$-axis satisfying $\mathbf{c} \cdot \mathbf{a}=9$ and $\mathbf{c} \cdot \mathbf{b}=-4$. If inclination of $\mathbf{c}$ with $X$-axis and $\gamma$-axis is $\alpha$ and $\beta$ respectively, then which of the following is not true?