Determine whether the following statements are true and give an explanation or counterexample. a. Jos travels from

Determine whether the following statements are true and give an explanation or counterexample. 

a. José travels from point A to point B in the plane by following vector u, then vector v, and then vector w. If he starts at A and follows w, then v, and then u, he still arrives at B.

b. Maria travels from A to B in the plane by following the vector u. By following -u, she returns from B to A.

c. |u + v| ≥ |u|, for all vectors u and v.

d. |u + v| ≥ |u| + |v|, for all vectors u and v.

e. Parallel vectors have the same length.

f. Ifthen A = C and B = D.

g. If u and v are perpendicular, then |u + v| = |u| + |v|.

h. If u and v are parallel and have the same direction, then |u + v| = |u| + |v|.

Transcribed Image Text:

AB = CD,