# Thread: the component form of a vector + unit vector with same direction

1. ## the component form of a vector + unit vector with same direction

i need to;

write in component for the vector with the initial point P(6,2) and the final point Q(3,7)

I think the answer is PQ = -3i +5j is that right?

later in the question I have to write a unit vector with the same direction and I have no idea how to do this.

Thanks for the help

ES

2. Originally Posted by El Sparko
i need to;

write in component for the vector with the initial point P(6,2) and the final point Q(3,7)

I think the answer is PQ = -3i +5j is that right?
Yes, that is correct.

later in the question I have to write a unit vector with the same direction and I have no idea how to do this.

Thanks for the help

ES
A unit vector has length 1. PQ is not a unit vector because its length is $\sqrt{3^2+ 5^2}= \sqrt{9+ 25}= \sqrt{34}$
You can change the length of a vector while not changing the direction by multiplying or dividing both components by the same number. And you can change the length to 1 by dividing by $\sqrt{34}$.

3. Originally Posted by HallsofIvy
A unit vector has length 1. PQ is not a unit vector because its length is $\sqrt{3^2+ 5^2}= \sqrt{9+ 25}= \sqrt{34}$
You can change the length of a vector while not changing the direction by multiplying or dividing both components by the same number. And you can change the length to 1 by dividing by $\sqrt{34}$.
dividing what part by \sqrt{34} ?

4. I said "dividing both components" of -3i+ 5j by $\sqrt{3}$.