# Homework help on vectors please

## Homework Statement

http://imgur.com/a/Yq8pW

## Homework Equations

projection u onto v: ((u x v)/(||v||^2)) x v
Unit vector: u/||u||

## The Attempt at a Solution

For number 2, I absolutely do not know how to set up the problem. I do not know what vectors to use, I assumed F vector to be <0.00375, 0.00625> and v vector to be <3 , 5> and plug them into the projection formula- projection u onto v: ((u x v)/(||v||^2)) x v-but that seems wrong since the teacher addressed that I find the vector of V, magnitude of vector V, and find unit vector so it should be <3, 5>/(sqrt 34) but how do I find the angle off of that?

jedishrfu
Mentor
Do you know about the vector dot product and what it represents?

Do you know about the vector dot product and what it represents?

I can find the angle between the vectors. Yes? But what I am confused about is what vectors to use.

jedishrfu
Mentor
You have F in i,j,k form and you should have v in i,j,k form.

• wicked1977
You have F in i,j,k form and you should have v in i,j,k form.

I think I got it! Except that the question states that the vector V is in the xy plane:
cos^-1((<3 , 5> x <0.00375 , 0.00625>)/(sqrt34 x sqrt 50))=89.94

jedishrfu
Mentor
Vector F=<3,5,4>/sqrt(3^2 + 5^2 + 4^2) * 800

so the unit vector for F is: Funit=<3,5,4> / sqrt(3^2 + 5^2 + 4^2) = <3,5,4> / (5*sqrt(2))

and unit vector Vunit = <3,5,0> / sqrt(3^2 + 5^2 + 0^2) = <3,5,0> / sqrt(34)

Funit . Vunit = (3^2 + 5^2 + 0*4) / (5*sqrt(2)*sqrt(34))

I didn't get 89.94 degrees for the angle.

• wicked1977
Vector F=<3,5,4>/sqrt(3^2 + 5^2 + 4^2) * 800

so the unit vector for F is: Funit=<3,5,4> / sqrt(3^2 + 5^2 + 4^2) = <3,5,4> / (5*sqrt(2))

and unit vector Vunit = <3,5,0> / sqrt(3^2 + 5^2 + 0^2) = <3,5,0> / sqrt(34)

Funit . Vunit = (3^2 + 5^2 + 0*4) / (5*sqrt(2)*sqrt(34))

I didn't get 89.94 degrees for the angle.

Did not realize I had to multiply my F vector by 800. And based on your solution, the angle is found to be 34.4. Thanks much!

jedishrfu
Mentor
In this case, there was a shortcut way too. If you notice that F, v and the 4k z component of F form a right triangle with F as the hypotenuse so that the sin of the angle must be 4/magnitude(F) = 4/sqrt(50) and hence its 34.4 degrees.