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15 cards from this deck
Magnitude and direction
i^\hat{i}i^ and j^\hat{j}j^
Ax=AcosθA_x = A \cos \thetaAx=Acosθ
Ay=AsinθA_y = A \sin \thetaAy=Asinθ
Place tail of B⃗\vec{B}B at head of A⃗\vec{A}A
Resultant vector R⃗\vec{R}R
(Ax+Bx)i^+(Ay+By)j^(A_x + B_x) \hat{i} + (A_y + B_y) \hat{j}(Ax+Bx)i^+(Ay+By)j^
∣A⃗∣=Ax2+Ay2|\vec{A}| = \sqrt{A_x^2 + A_y^2}∣A∣=Ax2+Ay2
θ=tan−1(AyAx)\theta = \tan^{-1} \left(\frac{A_y}{A_x}\right)θ=tan−1(AxAy)
∣A⃗∣∣B⃗∣cosθ|\vec{A}| |\vec{B}| \cos \theta∣A∣∣B∣cosθ
AxBx+AyByA_x B_x + A_y B_yAxBx+AyBy
∣A⃗∣∣B⃗∣sinθ|\vec{A}| |\vec{B}| \sin \theta∣A∣∣B∣sinθ
Right-hand rule
Resultant force is zero: ∑F⃗=0⃗\sum \vec{F} = \vec{0}∑F=0
W=F⃗⋅d⃗W = \vec{F} \cdot \vec{d}W=F⋅d
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