A force is given as F=x+5y-z. How do you calculate the magnitude of the force in the direction of the vector A=-3x+2y-2z?

1 Answer
Aug 8, 2018

FA=91717

Explanation:

We can use dot products!
In general,
FAA=FA
where FA is the component of the force along A.

This may be easier to see if we just think of normalizing A s.t. a=AA. Hence we can easily see that,

Fa=Fa

Using the first equation, we can easily calculate both known values:
FA=13+52+21=9
AA=(3)2+22+(2)2=17=A2

hence
FA17=9FA=91717

our final answer.