Question

PLEASE HELP WITH THIS VECTORS PROBLEM!



Given that |U|=4 and |V|=5 and the angle between U and V is 120 degrees, determine the unit vector in the same direction as U+V.

Please show all work, thanks :)

Answer 1

there are a number of ways to do this; if you are comfortable with the law of cosines you can get the length of u+v

Answer 2

Should I draw that?

Answer 3

probably

Answer 4

and I U is 4, V is 5 and theta is 120 right?

Answer 5

basically, but...
make sure you keep in mind the distinction between U and |U|
the first is a vector with a direction, whereas you mean that the \(length\) of the vector |U|=4

Answer 6

Ok, Ive drawn it, now what do I do?

Answer 7

do you know the law of cosines?

Answer 8

I don't remember it

Answer 9

http://en.wikipedia.org/wiki/Law_of_cosines

Answer 10

in our situation we have two sides and an angle, so we can apply the law to find the length of the third side.
Let us call the resultant vector \(\vec u+\vec v=\vec w\)
we then get from the cosine law\[\|\vec w\|^2=\|\vec u\|^2+\|\vec v\|^2-2\|\vec u\|\|\vec v\|\cos\theta\]

Answer 11

Ok, I see... this looks confusing

Answer 12

we can drop some of the symbols if they scare you
these are just the given numbers; remember that \(\|\vec u\|=5\) is just the given length of the vector.
That lets us use it as a side of the triangle.

Answer 13

the resultant vector is w=u+vwe are going to apply the law of cosines to find that length