A particle moves along the space curve

MATHEMATICS · Single correct · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

A particle moves along the space curve r(t)=⟨(1+t)cos⁡t,(1+t)sin⁡t,t2⟩\mathbf r(t)=\langle(1+t)\cos t,(1+t)\sin t,t^{2}\rangle. Its velocity is v(t)=r′(t)\mathbf v(t)=\mathbf r'(t), and its angular momentum about the origin is defined as L(t)=r(t)×v(t)\mathbf L(t)=\mathbf r(t)\times\mathbf v(t). What is L′(t)\mathbf L'(t) evaluated at t=0t=0? (a) ⟨0,−2,0⟩\langle 0,-2,0\rangle (b) ⟨0,2,−2⟩\langle 0,2,-2\rangle (c) ⟨0,−2,2⟩\langle 0,-2,2\rangle (d) ⟨0,0,1⟩\langle 0,0,1\rangle

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