Math E-21a – Fall 2009 – HW #1 problems Due in class on Thurs, Sept 10: Section 9.1: 8. Find the distance from (3, 7,–5) to each of the following. (a) The xy-plane (b) The yz-plane (c) The xz-plane (d) The x-axis (e) The y-axis (f) The z-axis 12. Find an equation of the sphere that passes through the origin and whose center is (1, 2, 3). 14. Show that the equation 2224448161xyzxyrepresents a sphere, and find its center and radius. 34. Consider the points Psuch that the distance from Pto A(–1, 5, 3) is twice the distance from Pto B(6, 2,–2). Show that the set of all such points is a sphere, and find its center and radius. Section 9.2: 20. Find a vector that has the same direction as 2,4,2but has length 6. 24. Velocities have both magnitude and direction and thus are vectors. The magnitude of a velocity vector is called speed. Suppose that a wind is blowing fromthe direction N45W at a speed of 50 km/h. (This means that the direction from which the wind blows is 45west of the northerly direction.) A pilot is steering a
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