# Force Vector Magnitude Distance

Justabeginner

## Homework Statement

A force of f= i + 2j- 3k is applied to a particle that moves 10 feet in the direction of i + j. How much work is done?

## Homework Equations

W= ||F|| dot product d

## The Attempt at a Solution

D= 10 cos 45 i + 10 sin 45 j
D= 5sqrt(2) i + 5 sqrt(2) j
F= i + 2j - 3k

W= ||F|| dot product d
W= sqrt(14) dot product (5sqrt(2)i + 5sqrt(2)j)
W= 5sqrt(28) + 5 sqrt(28)
W= 10sqrt(28)
W= 20sqrt(7)
Is this even right? Thanks!

Homework Helper
Gold Member

## Homework Statement

A force of f= i + 2j- 3k is applied to a particle that moves 10 feet in the direction of i + j. How much work is done?

## Homework Equations

W= ||F|| dot product d

##\| F\|## is a scalar and you can't dot a scalar and a vector.

## The Attempt at a Solution

D= 10 cos 45 i + 10 sin 45 j
D= 5sqrt(2) i + 5 sqrt(2) j
F= i + 2j - 3k

W= ||F|| dot product d
W= sqrt(14) dot product (5sqrt(2)i + 5sqrt(2)j)
W= 5sqrt(28) + 5 sqrt(28)
W= 10sqrt(28)
W= 20sqrt(7)
Is this even right? Thanks!

No, it is not correct. You have F and D correct. Look up the correct formula for work.