CALCULATE THE RESULTANT OF EIGHT COPLANAR FORCES OF VALUES 10N,12N,14N,13N,17N, 14N,12N,17N ACTING ON AN OBJECT AT O.
If they are co planar, draw x and y axes on the plane.
Then each of your vectors, vector n, is at some angle Tn counterclockwise from the x axis
It then has x and y components
for the first one for example
10 cos T1 in x direction
10 sin T1 in y direction
for the second
12 cos T2 in x direction
12 sin T2 in y direction
then
add up all 8 of the x components
Sumx = 10 cos T1 + 12 cos T2 ..... +17 cos T8
and tthe y
Sumy = 10 sin T1 +12 sin T2 ..... +17 sin T8
now your final magnitude is sqrt (Sumx^2 + Sumy^2)
and your angle from the x axis is
tan^-1 (Sumy/Sumx)