Addition of 3d force vectors to find resultant

[TW Cantor]

Homework Statement

A force of 5N acts along the vector (-4,-3,-1)
A force of 2N acts along the vector (-3,-6,5)
A force of 4N acts along the vector (-9,-1,8)

find the resultant force vector.

Homework Equations

The Attempt at a Solution

i tried to multiply the vectors by the force acting along them and then adding them together but that didnt work. other than that I am unsure as to how to start this particular question?

 

[jhae2.718]

You have magnitudes of forces and a list of vectors. What kind of vectors can you find so that, if you multiply the magnitude of the force and the vector, the resulting vector will be in the direction of the original vector but has the magnitude of the force?

 

[TW Cantor]

im not really sure what you mean? are you saying that if i take the 5N vector acting along (-4,-3,-1) then i can say that that is equal to (-20,-15,-5)?

 

[jhae2.718]

im not really sure what you mean? are you saying that if i take the 5N vector acting along (-4,-3,-1) then i can say that that is equal to (-20,-15,-5)?

No. When you multiply <-4,-3,-1> by 5 N, the resulting vector is not the force vector. <-4,-3,-1> has it's own magnitude which affects the magnitude of the force vector so that it is not 5N.

What can you do to get a vector that is in the direction of <-4,-3,-1> and has a magnitude equal to 5 N?

 

[alexfloo]

Here's a hint, start by finding the magnitude of <-4,-3,-1>. Then you can use that information to get rid of that magnitude, and then multiply away.

 

[TW Cantor]

well you can say that:
5=((-4*x)^2+(-3*x)^2+(-1*x)^2)^0.5

where x is a constant. once you find x you can multiply the original vector by it to get a vector with magnitude 5 in that direction

 

[jhae2.718]

Are you familiar with unit vectors?

 

[TW Cantor]

arent unit vectors = (a.b)/(|a.b|)?

would i convert them all into their unit vectors and then multiply by the force acting along them?

 

[jhae2.718]

would i convert them all into their unit vectors and then multiply by the force acting along them?

Yes. All you need to do is divide each vector by its magnitude and then multiply by the force to get force vectors you can sum.

Recall $$\hat{a} = \frac{\vec{a}}{|\vec{a}|}$$

 

[TW Cantor]

ahh ok, I've got it now :-) thanks a lot