HW 1 - Math E-21a Fall 2009 HW #1 problems Due in class on...

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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 222 4 4 4 8 16 1 x yzxy   represents a sphere, and find its center and radius. 34. Consider the points P such that the distance from P to A (–1, 5, 3) is twice the distance from P to 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 2,4,2 but 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 from the direction N45 W at a speed of 50 km/h. (This means that the direction from which the wind blows is 45 west of the northerly direction.) A pilot is steering a
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