Question 7
In the three dimensional Cartesian space with $\mathbf i$, $\mathbf j$ and $\mathbf k$ denoting the unit vectors along three perpendicular directions in a clockwise manner, the line $\ell$ with equation given by $\mathbf r\times(\mathbf i+2\mathbf j+3\mathbf k)=5\mathbf i-13\mathbf j+7\mathbf k$ intersects the plane $\Pi$ with equation $x+y+z=16$ at the point $(a,b,c)$. Find the value of $a+b+c$.