Question

Let vector u = (a, b) and vector v = (c, d). If the vectors are located as shown in the graph, then

A) ab = -cd
B) ac = -bd
C) a + b = c + d
D) a + d = b + c

Answer 1

We have the following vectors:
u = (a, b)
v = (c, d)
We observe that the vectors form an angle of 90 degrees.
Therefore, the product u.v is equal to zero.
We have then:
u.v = (a, b). (c, d) = 0
u.v = ac + bd = 0
ac = -bd
Answer:
B) ac = -bd