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

• Nov 5th 2009, 04:25 AM
El Sparko
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
• Nov 5th 2009, 04:44 AM
HallsofIvy
Quote:

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.

Quote:

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 $\sqrt{34}$.
• Nov 5th 2009, 05:07 AM
El Sparko
Quote:

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} ?
• Nov 5th 2009, 08:23 AM
HallsofIvy
I said "dividing both components" of -3i+ 5j by $\sqrt{3}$.
• Nov 5th 2009, 04:03 PM
El Sparko