Rectangular Cartesian Components

SmartSelect_20230928_133847_Samsung Notes.jpg

$\vec{F} = F_{x} \hat{i} + F_{y} \hat{j}$
- $F_{x} = F \cos θ$
- $F_{y} = F \sin θ$
$\hat{i}$ unit vector along x-direction
$\hat{j}$ unit vector along y-direction
$F = \sqrt{F_{x}^{2} + F_{y}^{2}}$
$\tan θ = \frac{F_{y}}{F_{x}}$
$\vec{R} = \vec{P} + \vec{Q} + \vec{S}$
$R_{x} \hat{i} + R_{y} \hat{j} = P_{x} \hat{i} + P_{y} \hat{j} + Q_{x} \hat{i} - Q_{y} \hat{j} - S_{x} \hat{i} + S_{y} \hat{j}$
$R_{x} \hat{i} + R_{y} \hat{j} = (P_{x} + Q_{x} - S_{x}) \hat{i} + (P_{y} - Q_{y} + S_{y}) \hat{j}$
$\tan θ = \frac{\sum F_{y}}{\sum F_{x}} = \frac{P_{y} - Q_{y} + S_{y}}{P_{x} + Q_{x} - S_{y}}$
$| \vec{R} | = \sqrt{{(P_{x} + Q_{x} - S_{x})}^{2} + {(P_{y} - Q_{y} + S_{y})}^{2}}$