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

El Sparko · #1 $Old$ November 5th, 2009, 06:25 AM

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

HallsofIvy · #2 $Old$ November 5th, 2009, 06:44 AM

Quote:

Originally Posted by El Sparko $View Post$

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 $\sqrt{34}$ .

El Sparko · #3 $Old$ November 5th, 2009, 07:07 AM

Quote:

Originally Posted by HallsofIvy $View Post$

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} ?

HallsofIvy · #4 $Old$ November 5th, 2009, 10:23 AM

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

El Sparko · #5 $Old$ November 5th, 2009, 06:03 PM

yes, sorry I misread your first post. thanks very much for your help.