Questions on Algebra: Introduction to vectors, addition and scaling answered by real tutors!

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Question 88188: A vector has the following initial and terminal points respectively:
initial point (-1,2)
terminal point (4,6)
What is the position vector?: A vector has the following initial and terminal points respectively:
initial point (-1,2)
terminal point (4,6)
What is the position vector?
Answer by jim_thompson5910(9390) About Me  (Show Source):
You can put this solution on YOUR website!
If you want to find the vector from the point (-1,2) to (4,6), simply subtract the vector from like this.



So the position vector is



Notice how when we subtract vectors, the resulting vector is a vector from the tip of the first vector to the tip of the second one. To prove that is the position vector, simply shift the resulting vector to have an initial point at (0,0) (the shifted vector is shown in green). Here you can see that the shifted vector has a terminal point at (5,4). This verifies our answer

drawing(800, 800, -5+2, 5+2, -5+2, 5+2,<BR> graph(800, 800, -5+2, 5+2, -5+2, 5+2, 0),<BR> locate(2,3,Vector A),<BR> locate(-0.5,1,Vector B),<BR> locate(4,6,Position Vector),<BR> locate(3.2,4.2,Position Vector With Initial Point At Origin),<BR> blue(arrow(0,0,4,6)),<BR> red(arrow(0,0,-1,2)),<BR> red(arrow(-1,2,4,6)),<BR> green(arrow(0,0,4--1,6-2)) <BR> ) Plot of , , and the resulting vector . Notice how the shifted vector is equivalent to the position vector.