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Resolving vectors question from an old M1 Paper

We've been given a few M1 past papers to do over half term, and this one just happens to be from June 1995 so as you'd expect I can't find support for it anywhere on the internet.

Q7 is a resolving vectors question and while I've got part a fine, part b is 9 marks and is completely stumping me because I don't know how to start -

"The force F is the resultant of two forces P and Q. The line of action of P is parallel to the vector (2i - j). The line of action of Q is parallel to the vector (i +3j). Find in terms of i and j, (i) the force P, (ii) the force Q."

Force F in this case is (9i + 13j)

any help would be appreciated!!! :smile:
Reply 1
Avatar for atsruser
atsruser
11
Original post by velkyr

"The force F is the resultant of two forces P and Q. The line of action of P is parallel to the vector (2i - j). The line of action of Q is parallel to the vector (i +3j). Find in terms of i and j, (i) the force P, (ii) the force Q."

Force F in this case is (9i + 13j)



So you must have:

F⃗=P⃗+Q⃗\vec{F} = \vec{P}+\vec{Q}

and also that P⃗\vec{P} is a multiple of 2i−j2\bold{i}-\bold{j} with a similar statement for Q⃗\vec{Q}.

Express that all of that algebraically and it should be clear how to solve the problem.
Reply 2
Avatar for the bear
the bear
20
you end up with simultaneous equations to find the components of P and Q
Reply 3
Avatar for velkyr
velkyr
OP
1
Original post by the bear
you end up with simultaneous equations to find the components of P and Q

so with these simultaneous equations, would I have an equation for the horizontal component and one for the vertical component?

as in -

for the horizontal : 9 = 2k + m
for the vertical : 13 = -k + 3m ?
Reply 4
Avatar for the bear
the bear
20
Original post by velkyr
so with these simultaneous equations, would I have an equation for the horizontal component and one for the vertical component?

as in -

for the horizontal : 9 = 2k + m
for the vertical : 13 = -k + 3m ?


:dance:

yes
Reply 5
Avatar for velkyr
velkyr
OP
1
Original post by the bear
:dance:

yes

Ahhhh that makes a lot more sense now!! Thank you. :yep:
Reply 6
Avatar for ftap12
ftap12
wait , can u please fully explain how to do this because i am still stuck :P , haha sorry i did this question today and do not know what i am doing , thank you

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