Exercise I: Fruit ninja 1. Determine the surface S given by the equation x 2 − 4x + y 2 − 2y + z 2 − 6z = 2. 2. Find an equation
of the plane P going through the points (1, 1, 1), (1, 4, −2), and (−1, 0, 4), of the form ax + by + cz + d = 0. 3. Clearly, the intersection of S and P is a circle. Compute the radius r of this circle. You may want to draw a picture first, and use a result seen in class!
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