The shortest distance of the plane 12 + 4y + 3z = 327, from the sphere x² + y² + z² + 4x − 2y − 6z = 155, is equal to:

13 units

Center and radius of given sphere are (–2, 1, 3) and 13 unit respectively.

Now, distance of center of the sphere from the given plane

= $\frac{|-24+4+9-327|}{\sqrt{12^2+4^2+3^2}}$ = 26 units

∴ Shortest distance = (26 – 13) = 13 units