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Numerade Educator



Problem 54 Hard Difficulty

If $ r = \langle x, y, z \rangle $ , $ a = \langle a_1, a_2, a_3 \rangle $ and $ b = \langle b_1, b_2, b_3 \rangle $ show that the vector equation $ (r - a) \cdot (r - b) = 0 $ represents a sphere, and find its center and radius.


Center $\left(\frac{a_{1}+b_{1}}{2}, \frac{a_{2}+b_{2}}{2}, \frac{a_{3}+b_{3}}{2}\right) ;$ radius $\frac{|\mathbf{a}-\mathbf{b}|}{2}$


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Video Transcript

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