I've attempted to solve the problem, but I got $\langle \frac{1}{\sqrt{\frac{29}{4}}}, \frac{5}{\sqrt{\frac{29}{4}}}\rangle$, which is incorrect. There is not a similar problem in my textbook that I can reference.
I know that to find a unit vector, we first find the length/magnitude of the given vector, and multiply $$1/\sqrt{magnitude}$$ by the original vector.
$$L = \sqrt{x^2 + y^2}.$$
Can anyone give me any ideas on how to solve this problem?
Find the unit vector that has the same direction as the vector from the point A = (-1,2) to the point B = (3,3).
Thank you in advance.
Best Answer
The vector that goes from $A$ to $B$ is the vector $B-A$: to see this, notice that if you add vectors using the parallelogram rule, then adding the vector $V$ you are looking for to $A$ should give you $B$, so $A+V = B$, giving you $V=B-A$.
So the vector you are looking for is $V = B-A = (3,3) - (-1,2) = (4,1)$.
Now that you know the vector, finding the unit vector in the same direction is done as you indicate: find the magnitude of $V$, divide by the magnitude.
(Looks like you took $A+B$ instead of $B-A$)