# Math Help - I could use some help on this Calculus problem

1. ## I could use some help on this Calculus problem

The problem reads: A constant force with vector representation F=10i+18j-6k moves an object along a straight line from the point (2,3,0) to the point (4,9,15). Find the work done if the distance is measured in meters and the magnitude of the force is measured in Newtons. From this I got the force by using sqrt(10^2+18^2+(-6)^2)=2*sqrt(115)*N Additionally I got the distance to be sqrt((4-2)^2+(9-3)^2+(15-0)^2)=sqrt(265)*m And because J=m*N I got the answer (2*sqrt(115)*N)*(sqrt(265)*m)=10*sqrt(1219) J However, the answer book gives is 38 J so could someone tell me what I'm doing wrong

2. Is the force parallel to the movement of the point?

The problem reads: A constant force with vector representation F=10i+18j-6k moves an object along a straight line from the point (2,3,0) to the point (4,9,15). Find the work done if the distance is measured in meters and the magnitude of the force is measured in Newtons. From this I got the force by using sqrt(10^2+18^2+(-6)^2)=2*sqrt(115)*N Additionally I got the distance to be sqrt((4-2)^2+(9-3)^2+(15-0)^2)=sqrt(265)*m And because J=m*N I got the answer (2*sqrt(115)*N)*(sqrt(265)*m)=10*sqrt(1219) J However, the answer book gives is 38 J so could someone tell me what I'm doing wrong
Work:

$
\bold{W}=\int \bold{F}.\bold{dx}
$

In this case we have constant force and a straight line so this reduces to:

$
\bold{W}=\bold{F}.\bold{d}
$

where $\bold{d}=(4,9,15) - (2,3,0)$

RonL