Vector Algebra

If the position vectors of the vertices $A, B, C$ of a triangle are $3 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}-\hat{\mathbf{k}}, \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+\hat{\mathbf{k}}, 5(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}})$ respectively, then the magnitude of the altitude drawn from $A$ on to the side $B C$ is