It is known that, as shown in the figure, in the trapezoidal ABCD, ad ‖ BC, let ad = vector a, BC = vector B, e and f respectively on the waist AB and DC, and AE: be = DF: CF = 1:2 (1) Using the linear combination of vectors a and B to represent vector ef (2) Is EF parallel to ad? Why? (3) If ad = m, BC = n, find the length of EF

It is known that, as shown in the figure, in the trapezoidal ABCD, ad ‖ BC, let ad = vector a, BC = vector B, e and f respectively on the waist AB and DC, and AE: be = DF: CF = 1:2 (1) Using the linear combination of vectors a and B to represent vector ef (2) Is EF parallel to ad? Why? (3) If ad = m, BC = n, find the length of EF

1. B-2 / 3 (B-A) = 1 / 3B + 2 / 3A (→ not marked)
2. Yes, a and B have the same direction, B + a = 1 / 3 + 2 / 3a
3.1/3b+2/3a =1/3n+2/3m
(this answer is not standard and may not be correct. Check carefully.)