Troubleshooting 3D Vector Work: Solving Angle and Displacement Confusion

[hehedxd]

Homework Statement

A 5 N force which is along the direction vector (2,3,4) moves an object from A(1,-4,5)
to B(2,-1,3). What is the work done?

Relevant Equations

Dot product
W = F x d

I'm having trouble finding the angle and displacement

 

[PeroK]

Homework Statement:: A 5 N force which is along the direction vector (2,3,4) moves an object from A(1,-4,5)
to B(2,-1,3). What is the work done?
Relevant Equations:: Dot product
W = F x d

I'm having trouble finding the angle and displacement

The displacement is $A$ to $B$, isn't it? Do you really need the angle?

 

[hehedxd]

How would you find the displacement?
Also what do you do with the direction vector?

 

[PeroK]

How would you find the displacement?
Also what do you do with the direction vector?

I would ask myself how do I get from $A$ to $B$. I assume we are talking about a straight line path here.

I don't know what a "direction" vector is. There is a force vector and a displacement vector here.

 

[DrunkenUFOPilot]

Using 'x' is misleading. You want a _dot_ product.
Hint: you don't need to find any angles.

 

[hehedxd]

So i disregard the first vector given in the problem and get the dot product of a and b?

 

[PeroK]

So i disregard the first vector given in the problem and get the dot product of a and b?

No, you need the dot product of the force and displacement vectors:
$$W = \vec F \cdot \vec d$$

 

[DrunkenUFOPilot]

So i disregard the first vector given in the problem and get the dot product of a and b?

A and B are the starting and stopping points of the thing being pushed. Work is done by the force acting over that displacement.

 

[archaic]

What is the displacement vector @hehedxd ?

 

[hehedxd]

I think its the vector along which the force acts.

 

[archaic]

I think its the vector along which the force acts.

No, the displacement vector is the difference between the final position vector and the initial position vector. You have both given as A and B. Can you compute it?

 

[hehedxd]

No can you help me

 

[archaic]

The initial position vector is $\vec A=(1,-4,5)$ and the final position vector is $\vec B=(2,-1,3)$. The displacement vector is $\vec s=\vec B-\vec A$. Can you compute it?

 

[hehedxd]

ok I got s = (1,3,-2) thanks

 

[archaic]

Great! Now, what you want is $W=\vec F\cdot\vec s=Fs\cos\theta$.
The problem statement is telling you that the force is in the direction of the vector $(2,3,4)$, so we know that the angle between $\vec F$ and $\vec s$ is the same as the angle between $(2,3,4)$ and $\vec s$.
Can you find that angle?

 

[hehedxd]

Wait I thought we didn't need angle.
I was going to find the vector that represents the force and use dot product

 

[PeroK]

Great! Now, what you want is $W=\vec F\cdot\vec s=Fs\cos\theta$.
The problem statement is telling you that the force is in the direction of the vector $(2,3,4)$, so we know that the angle between $\vec F$ and $\vec s$ is the same as the angle between $(2,3,4)$ and $\vec s$.
Can you find that angle?

To find the angle, you could always first compute the dot product!

 

[archaic]

Wait I thought we didn't need angle.
I was going to find the vector that represents the force and use dot product

Sure, you can also do that.

 

[archaic]

To find the angle, you could always first compute the dot product!

Yes, I was trying to lead him to that!

 

[hehedxd]

Ok thanks I got it now