Calculating a value of force using vectors?

[xllx]

A box is being pulled with a resultant force of (33i+96j)N by 3 people. Another person starts pulling the box with a force of (100i+pj)N. With all 4 people pulling the box, it moves in the direction of (12i +j). I need to work out the value of p.

For this would I add 100 and 33, and then divide by 12 to find the proportions of i. And then with that times it by the 1j to get what j is.
E.g.
100+33=133
133/12=11.1

1x11.1=11.1
96+j=11.1
j= -84.9

Or is this totally wrong?

Any help at all would be greatly appreciated. Many Thanks!

 

[Delphi51]

Correct!
Might be easier to follow if you put
33i+96j + 100i+pj = k(12i+j)
Separate the i part from the j part. Use the i part to evaluate k, then use it in the j part to find p.

 

[LowlyPion]

A box is being pulled with a resultant force of (33i+96j)N by 3 people. Another person starts pulling the box with a force of (100i+pj)N. With all 4 people pulling the box, it moves in the direction of (12i +j). I need to work out the value of p.

For this would I add 100 and 33, and then divide by 12 to find the proportions of i. And then with that times it by the 1j to get what j is.
E.g.
100+33=133
133/12=11.1

1x11.1=11.1
96+j=11.1
j= -84.9

Or is this totally wrong?

Any help at all would be greatly appreciated. Many Thanks!

That looks correct. Of course you are finding p and not j, but the method looks ok.