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{"ops":[{"insert":"Let \ud835\udc591 be the line that passes through \ud835\udc5d1 = (2,9,8) and \ud835\udc5d2 = (1,9,9) and let \ud835\udc592 be the line that passes through \ud835\udc5d3 = (1,1,1) and \ud835\udc5d4 = (2,5,4) a) Find out if the two lines intersect and if so, find the intersection point of \ud835\udc591 and \ud835\udc592 b) Let \ud835\udc46 be the sphere whose center is the intersection of \ud835\udc591 and \ud835\udc592 and whose radius is \ud835\udc5f = 4. Write the implicit representation of the sphere. c) Find the implicit representation of the two planes \ud835\udc431 and \ud835\udc432 that are tangent to the sphere \ud835\udc46 at the points of intersections of \ud835\udc591 towards \ud835\udc5d2 and \ud835\udc592 towards \ud835\udc5d4 , respectively.\n"}]}
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