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Vector Forces Issue

"Two forces F1 and F2 act on a particle P.
The force F1 is given by F1 = (-i +2j) N and F2 acts int he direction of the vector (i + j).

Given that the resultant of F1 and F2 acts in the direction of the vector (i+3j),

Find F2"

I didn't exactly understand how to attempt the question. It didn't stop me from trying however and got this:

Because Resultant = (i+3j) therefore

i + 3j = xi + yj + i + j
F1 direction is therefore 2j

I guess F1's direction somehow links back to finding F2??

Reply 1

RDKGames

Study Forum Helper

Original post by OJ Emporium

The resultant is not i+3j

You are told F1 explicitly, but you are not told what F2 is explcitly, you are merely given its direction and NOT the magnitude!

So you need to account for it by introducing a scalar quantity

k

...

Hence we have that

F_2 = k(\mathbf{i} + \mathbf{j})

.

NOW you can proceed to determine the resultant.

The goal is to now determine what

k

is as that tells us what our

F_2

is precisely.
So you want this resultant vector have the same direction as i+3j... so note that for ONE i component we go THREE up.This means that the j component is three times more than the i component. This is precisely the condition you need to put on your resultant vector in terms of k.