Why do I need to put the vector on the x axis in this problem? "3 forces act on...."

[Integrate]

Why do I need to put the vector on the x axis in this problem? "3 forces act on...."

Three forces act on an object. Two of the forces are at an angle of 100° to each other and have magnitudes 25 N and 12 N. The third is perpendicular to the plane of these two forces and has magnitude 4 N. Calculate the magnitude of the force that would exactly counterbalance these three forces.
In the solution manual it solves it by putting the force vector of 12N on the x- axis creating a resultant vector of
<25cos(100)+12+0 , 25sin(100)+0+0, 0+0+4>
Why do I need to place the force vector 12N on the x-axis? Couldn't I find the magnitude as
<25cos(100)+12cos(100)+0 , 25sin(100)+12sin(100)+0, 0+0+4> ?
Thank you!

 

[Dr.Peterson]

Three forces act on an object. Two of the forces are at an angle of 100° to each other and have magnitudes 25 N and 12 N. The third is perpendicular to the plane of these two forces and has magnitude 4 N. Calculate the magnitude of the force that would exactly counterbalance these three forces.
In the solution manual it solves it by putting the force vector of 12N on the x- axis creating a resultant vector of
<25cos(100)+12+0 , 25sin(100)+0+0, 0+0+4>
Why do I need to place the force vector 12N on the x-axis? Couldn't I find the magnitude as
<25cos(100)+12cos(100)+0 , 25sin(100)+12sin(100)+0, 0+0+4> ?
Thank you!

It is not necessary to put that vector on the x-axis; there are many ways you could assign a coordinate system to the problem.

But where are you putting the vectors? You have not explained your result, but it looks like you put the 25N and 12N vectors both in the same direction, which is not what the problem says! It says there is a 100° angle between them, not between each of them and the positive x-axis.

 

[Integrate]

Dude thank you so much.