Argh!
Sorry about that - I was in the midst of studying for my 7th final last night. Brain's not working too well anymore. Thank goodness only 1 final left.
Anyhow, scratch what I said about just adding the vectors together using a power cross. Use the vector method - you will get the right answer.
+2.00x120/-2.25x030
MOR = (+2.00/2) + (-2.25/2) = -0.125
Cx = (+2.00cos2(120)) + (-2.25cos2(030)) = -2.125
Cy = (+2.00sins(120)) + (-2.25sin2(030)) = -3.68
Cr = sqrt(-2.125sq + -3.68sq) = +-4.25
Theta(r) = 1/2tan(-3.68/-2.125) = 30 degrees
Resultant sphere:
Sr1 = MOR - C/2 = -0.125 - 4.25/2 = -2.25
Sr2 = MOR + C/2 = -0.125 + 4.25/2 = +2.00
The more positive resultant sphere is used for minus cylinder form while the more negative resultant sphere is used for plus cylinder form.
The degree resultant applies to the negative cylinder form of the combination (if the resultant degree was negative though, you'd have to add 180 to it and apply it to the plus cyl form and then use transposition to find the minus cyl form - if that makes sense).
So minus cyl form is: +2.00-4.25x030
Plus cyl form is: -2.25+4.25x120
My answers for your second problem using this method (but running on very little sleep are
😴 ):
Minus cylinder: +1.25-2.73x057 (+1.25-2.75x057)
Plus cylinder: -1.49+2.73x147 (-1.50+2.75x147)