Question

A force, f, of 25N is acting in the direcion of vector a = [6,11]
a) Find the unit vector in the direction of vector a
b)Find the cartesian vector representing the force, f, using your answer from aprt a.
c) The force f is exerted on an object moving from point (4,0) to point (15, 0) with distance in metres. Determine the mechanical work done.

Answer 1

Okay, so a unit vector is just a matter of dividing a vector by it's magnitude.

Answer 2

I managed to figure that portion after a bit, and I ended up with u = (6/sqrt37, 1/sqrt37)
But now, I have no idea how to find the cartesian vector for F, since there's no angle. >.<
Thank you for responding

Answer 3

Once you have it as a unit vector, you can scalar multiply the force

Answer 4

That is likely what they want.

Answer 5

..Can you briefly go through the steps for me? Please?
I hadn't realized you can approach it as a scalar when it's in a unit vector..

Answer 6

Well, when you multiply a vector by a scalar, its direction does not change.

Answer 7

However it's new magnitude ends up being the old magnitude times the scalar

Answer 8

So, the nice thing about a unit vector is that when you do scalar multiplication, the old magnitude was 1, meaning that the new magnitude is just the value of the scalar.

Answer 9

Oh, I guess I kind of understand it.
Thank you!