Mathematics

Mathematics

Problem

In a computer graphics simulation, two expanding circular ripples are modeled. Ripple AA is centered at vector position a⃗=2i+2j\vec{a} = 2\mathbf{i} + 2\mathbf{j} with radius 33. Ripple BB is centered at vector position b⃗=6i+5j\vec{b} = 6\mathbf{i} + 5\mathbf{j} with radius rr. Using vector operations (dot product/magnitude), determine the radius rr required for the ripples to intersect orthogonally.

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