Given are four concurrent forces: 10 N east, 20 N north, 15 N west, 25 N south. What is the direction of the resultant force?
South-west
To find the resultant of concurrent forces we resolve them along two perpendicular axes (East–West and North–South), add algebraically, and then interpret the signs. Let East and North be positive.
Horizontal (East–West) components:
- 10 N East (+10) and 15 N West (−15)
- Sum = +10 − 15 = −5 N, i.e. 5 N directed West.
Vertical (North–South) components:
- 20 N North (+20) and 25 N South (−25)
- Sum = +20 − 25 = −5 N, i.e. 5 N directed South.
The resultant therefore points partly West and partly South, which places it in the South-West quadrant. That is why South-West is correct.
Its magnitude is R = √((−5)² + (−5)²) = √(25 + 25) = √50 = 5√2 ≈ 7.07 N, and because the West and South components are equal, the direction is exactly 45° below the West axis (i.e. midway between South and West).
The other directions are ruled out by the signs: North-east would need both components positive (net East and net North), South-east would need a net East component, and North-west would need a net North component. Here both net components are negative (West and South), so only South-West fits.
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