# Work done (Question on Vectors)

• May 23rd 2011, 11:31 AM
Tron
Work done (Question on Vectors)
Can someone help me with this one, please.

Find the work done by a two dimensional force of 2[units] in the direction of the line y= (3x-3)(upward) in moving an object from point Q=(1,-2,-3) to point P=(-1,0,1).
• May 23rd 2011, 04:49 PM
skeeter
Quote:

Originally Posted by Tron
Can someone help me with this one, please.

Find the work done by a two dimensional force of 2[units] in the direction of the line y= (3x-3)(upward) in moving an object from point Q=(1,-2,-3) to point P=(-1,0,1).

displacement vector $\displaystyle \vec{QP} = -2i + 2j + 4k$

force vector $\displaystyle \vec{F} = \frac{2}{\sqrt{10}}i + \frac{6}{\sqrt{10}}j$

determine the scalar product of the two vectors
• May 23rd 2011, 05:44 PM
Tron
Quote:

Originally Posted by skeeter
displacement vector $\displaystyle \vec{QP} = -2i + 2j + 4k$

force vector $\displaystyle \vec{F} = \frac{2}{\sqrt{10}}i + \frac{6}{\sqrt{10}}j$

determine the scalar product of the two vectors

Thx a lot

How did you calculate the force vector?
• May 23rd 2011, 05:58 PM
skeeter
Quote:

Originally Posted by Tron
Thx a lot

How did you calculate the force vector?

I picked two points on the line ... (0,-3) and (1,0)

direction of the force vector is ...

$\displaystyle i + 3j$

unit vector in that direction is ...

$\displaystyle \frac{i+3j}{\sqrt{1^2 + 3^2}}$

finally, multiply the unit vector by the magnitude of F.