Answer to Question #314911 in Math for math student

Question

Let 𝑙1 be the line that passes through 𝑝1 = (2,9,8) and 𝑝2 = (1,9,9) and let 𝑙2 be the line that passes through 𝑝3 = (1,1,1) and 𝑝4 = (2,5,4) a) Find out if the two lines intersect and if so, find the intersection point of 𝑙1 and 𝑙2 b) Let 𝑆 be the sphere whose center is the intersection of 𝑙1 and 𝑙2 and whose radius is 𝑟 = 4. Write the implicit representation of the sphere. c) Find the implicit representation of the two planes 𝑃1 and 𝑃2 that are tangent to the sphere 𝑆 at the points of intersections of 𝑙1 towards 𝑝2 and 𝑙2 towards 𝑝4 , respectively.

Answer 1

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