SOLUTION: This was a two part question. I figured out the answer for A but not B. Find components for the following vectors AB : (a) A = (1,2) and B = (3,-7) My answer is: from A to B [

Algebra ->  Formulas -> SOLUTION: This was a two part question. I figured out the answer for A but not B. Find components for the following vectors AB : (a) A = (1,2) and B = (3,-7) My answer is: from A to B [      Log On


   



Question 146952: This was a two part question. I figured out the answer for A but not B.
Find components for the following vectors AB :
(a) A = (1,2) and B = (3,-7)
My answer is: from A to B [-1,4]
(b) A = (2,3) and B = (2 + 3t, 3-4t)

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Your answer for A is not correct.
The vector AB should be able to lead you from A to B.
Look at it this way.
x%5BA%5D%2Bx%5BAB%5D=x%5BB%5D
for the x component and
y%5BA%5D%2By%5BAB%5D=y%5BB%5D
for the y component of the vector.
You can then re-arrange those equations and determine the x and y components of the vector AB.
x%5BAB%5D=x%5BB%5D-x%5BA%5D
and
y%5BAB%5D=y%5BB%5D-y%5BA%5D
Using the values from A.
x%5BAB%5D=x%5BB%5D-x%5BA%5D
x%5BAB%5D=3-1
x%5BAB%5D=2
y%5BAB%5D=y%5BB%5D-y%5BA%5D
y%5BAB%5D=-7-2
y%5BAB%5D=-9
[AB]=[2,-9]
If I start at (1,2) on the grid, I need to move 2 units to the right
(positive x) and move 9 units down (negative y) to reach point (3,-7).
b) The method is the same,
For the x component,
x%5BAB%5D=x%5BB%5D-x%5BA%5D
x%5BAB%5D=2%2B3t-2
x%5BAB%5D=3t
For the y component,
y%5BAB%5D=y%5BB%5D-y%5BA%5D
y%5BAB%5D=3-4t-3
y%5BAB%5D=-4t
[AB]=[3t,-4t]