Mathematics - Vector Question with Solution | TestHub

Let $\vec{p}=2\hat{i}+\hat{j}+3\hat{k}$ and $\vec{q}=\hat{i}-\hat{j}+\hat{k}$. If for some real numbers $\alpha ,\beta$, and $\gamma$, we have $15\hat{i}+10\hat{j}+6\hat{k}=\alpha (2\vec{p}+\vec{q})+\beta (\vec{p}-2\vec{q})+\gamma (\vec{p}\times \vec{q})$ then the value of $\gamma$ is