Work done (Question on Vectors)

**Tron** · May 23rd 2011, 11:31 AM

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).

**skeeter** · May 23rd 2011, 04:49 PM

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

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

determine the scalar product of the two vectors

**Tron** · May 23rd 2011, 05:44 PM

Originally Posted by skeeter

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

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

determine the scalar product of the two vectors

Thx a lot

How did you calculate the force vector?

**skeeter** · May 23rd 2011, 05:58 PM

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 ...

$i + 3j$

unit vector in that direction is ...

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

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

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