Question

Given vector u= (3,-5) and the graph of vector v, find v-4u and express the results in terms of i and j

Answer 1

Answer: 22j

Explanation:

1) From the graph you can calculate the vector v as folllows:

Translation of the extreme (-5,0) to the origin (0,0) implies add 5 units to - 5.

Then, add 5 units to the x-coordinate of the other extreme: 7 + 5 = 12; and keep the y-coordinate, which is 2.

Therefore, the coordinates of the vector v are (12,2)

2) Now you can find the vector v - 4u applying the operations to the coordinates of the two vectors:

v - 4u = (12,2) - 4(3, -5) = (12,2) - (12,-20) = (12 - 12, 2 + 20) = (0,22)

3) Changing the notation in terms to i, j; that is  0i + 22j = 22j