# [SOLVED] Vectors: Work Question(Dot Product)

• Feb 16th 2009, 08:51 AM
narutoblaze
[SOLVED] Vectors: Work Question(Dot Product)
If a 10N force, acting in the direction of the vector (1, 1), moves an object from P(-2, 1) to Q(5, 6), calculate the work done. The distance is in metres.

The work formula is W = F dot D = |F||d|Cos(theta)

• Feb 16th 2009, 01:01 PM
earboth
Quote:

Originally Posted by narutoblaze
If a 10N force, acting in the direction of the vector (1, 1), moves an object from P(-2, 1) to Q(5, 6), calculate the work done. The distance is in metres.

The work formula is W = F dot D = |F||d|Cos(theta)

I hope this reply doesn't come too late ...

1. Calculate the vector $\vec F$ with $|\vec F| = 10$:

$\vec F = 10\cdot (1,1)\cdot \dfrac1{|(1,1)|} = (5\sqrt{2}\ ,\ 5\sqrt{2})$

2. Calculate the vector

$\overrightarrow{PQ} = \vec d =(5-(-2), 6-1) = (7, 5)$

3. As you've stated the work is

$W=\vec F \cdot \vec d$ That means:

$W = (5\sqrt{2}\ ,\ 5\sqrt{2}) \cdot (7, 5)=60\sqrt{2} \approx 84.85\ Nm$
• Feb 16th 2009, 01:31 PM
narutoblaze
Just in time thanks!(Bow)