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Need help on M1 question....
1. Two forces F1 and F2 act on a particle. The force F1 is parallel to the vector (i + j) and the force F2 is parallel to the vector (i +2j). Given that the resultant R of these two forces is of magnitude 15N and parallel to the vector (3i + 4j), find the magnitude of F1 and the magnitude of F2.
I have found the vector of the resultant R to be (9i + 12j), but I don't know how to find the magnitudes of F1 and F2.
I have found the vector of the resultant R to be (9i + 12j), but I don't know how to find the magnitudes of F1 and F2.
Reply 1
Thanks, been great help 
Reply 2
bilal_786
1. Two forces F1 and F2 act on a particle. The force F1 is parallel to the vector (i + j) and the force F2 is parallel to the vector (i +2j). Given that the resultant R of these two forces is of magnitude 15N and parallel to the vector (3i + 4j), find the magnitude of F1 and the magnitude of F2.
I have found the vector of the resultant R to be (9i + 12j), but I don't know how to find the magnitudes of F1 and F2.
I have found the vector of the resultant R to be (9i + 12j), but I don't know how to find the magnitudes of F1 and F2.
Let F1=a(i+j), F2=b(i+2j) and F3=c(3i+4j)
F1+F2=F
a(i+j)+b(i+2j)=c(3i+4j)
lFl=15N t. f. 5c=15<=>c=3
t. f. a(i+j)+b(i+2j)=9i+12j
Equating coefficients yields a+b=9, a+2b=12
t. f. a=6 and b=3
t. f. F1=6i+6j and F2=3i+6j
t. f. lF1l=6Sqrt[2] and lF2l=3Sqrt[5]
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