The initial and terminal points of a vector are given. Write the vector as a linear combination of the standard unit vectors i and j.

Question

initial point: (-2,1)

terminal point: (5,-5)

Answer 1

You want to ask yourself, in moving from the first point to the second:

1. how far do you travel in the X-dimension (positive or negative)
2. how far do you travel in the Y-dimension (positive or negative)

In x, you start at x =-2 and end up at x = 5

That is a change of +7

So your x-component is 7i

In y, you start at y = 1 and end up at y = -5

That is a change of -6

So your y-component is -6j

So the requested vector is:

7i - 6j