In rectangle ABCD, ab = 2, ad = 1, then vector AC × vector CD

In rectangle ABCD, ab = 2, ad = 1, then vector AC × vector CD

We should ask about the scalar product. The vector AC dot multiplies the module of the vector CD = AC × the module of the vector CD × cos (π - angle ACD)
Cos angle ACD = ad / AC, AC square = ad square + CD square, AC = root 5
Cos angle ACD = 2 / radical 5, cos (π - angle ACD) = - 2 / radical 5
Vector AC dot multiplication vector CD = radical 5 × 2 × (- 2 / radical 5) = - 4

In trapezoidal ABCD, ad ‖ BC, angle ABC = 60 °, ad = 1, BC = 2, P is the upper moving point of the line where the waist AB is located, then the minimum value of | 3 times vector PC + 2 times vector PD | is | 3 times vector PC + 2 times vector PD |?
It's better to have a picture. Do you use coordinates? Is the answer 2 root 13?

In trapezoidal ABCD, ad ∥ BC, angle ABC = 60 °, ad = 1, BC = 2, the condition is still uncertain, is the length of AB missed?