Let the plane \( 2x + 3y + z + 20 = 0 \) be rotated through a right angle about its line of intersection with the plane \( x - 3y + 5z = 8 \). If the mirror image of the point \( \left( 2, -\dfrac{1}{2}, 2 \right) \) in the rotated plane is \( B(a,b,c) \), then:
