Two forces `vecF_(1)=(3N)hati-(4N)hatj` and `vecF_(2)=-(1N)hati-(2N)hatj` act on a point object. In the given figure which of the six vectors represents `vecF(1)` and `vecF_(2)` and what is the magnitude of the net forces

Options

A. 4 and 8, sqrt(19)N`
B. 3 and 6,5N`
C. 5 and 7, `sqrt(40)N`
D. 2 and 6,7 N

Answer

C

Explanation

`vecF_(1)=(3N)hati-(4N)hatj`
This means (3N) along +x axis and (4N) along negative side of y axis. Hence vector 5 represents it.
`vecF_(2)=-(1N)hati-(2N)hatj`
This means (1N) along negative x-axis. (2N) along negative y-axis.
hence force
`|F|^(2)=(2)^(2)+(-6)^(2)=40`
`therefore |F|=sqrt(40)N`