Maths Question Help

Two forces F1 and F2 are given by the vectors F1 = (-3i - 4j) N and F2 = (pi - 3pj) N. The resultant of the forces F1 and F2 , R acts in a direction which is parallel to the vector (3i - 4j).
(i) Show that p = − 24/5

Do you know what a resultant is and what it means to be parallel to a vector?

Do you know what a resultant is and what it means to be parallel to a vector?

Dont agree with the solution as
i: -3-24/5
and
j: -3-4
are not in the ratio 3:-4. Theyre both negative and the magnitudes are not 3:4. Can you upload a pic of the question again?

Calculate the ij resultant and just use the simple ratio 3:-4

So would you do:
-3+p/-4-3p=3/-4

Edit - missed the p on the denominator.
Yes, youd do that. Willl check the soln again.

Ok could you please explain why we’re doing this as our teacher just told us the method without explaining why. Do the ratios symbolise the scalar multiple?

You would have done ratios (fractions) in ~y4? Saying that it is parallel to 3i -4j means the i component and the j component are in the ratio 3:-4, so every 3 you go along the i axis, you go down 4, so -4.
It could be made to sound harder, but thats all there is to it. The magnitude is irrelevant (6i -8j or -3i + 4j or ...), only the ratio of the terms is important. Another way of looking at it is the gradient of the line (or the tangent of the angle) must be the same, but this still amounts to 3:-4 or -4/3 (as grad and tan are y/x).

Thank you I understand now So it it basically this : -3+p:-4-3p=3:-4

Yes, I edited the previous post to mention grads and tan, but they're just i:j component ratios/fractions as well so whatever way you look at it its simply equating two ratios.