Vector Algebra

Let $\mathbf{a}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}$ be the position vector of a point $A$. Let $\mathbf{b}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}$ and $\mathbf{c}=\hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ be two vectors and $\mathbf{r}$ be a vector passing through the point $A(\mathbf{a})$ and parallel to the vector $\mathbf{b}$. If the projection of $\mathbf{r}$ on $\mathbf{c}$ is $\frac{9}{\sqrt{6}}$, then $|\mathbf{r}|=$