Multivariable Calculus Quiz
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VECTORS AND GEOMETRY IN 3D
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A vector v⃗\vec{v} begins at the origin and ends at a point P(a,b,c)P(a,b,c) on the surface of a sphere of radius RR centered at the origin. Let u⃗=⟨a,b,0⟩\vec{u} = \langle a, b, 0 \rangle be the projection of v⃗\vec{v} onto the xyxy-plane. If the magnitude of u⃗\vec{u} is half the magnitude of v⃗\vec{v}, what is the absolute value of the zz-component, ∣c∣|c|, in terms of RR?
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