GE 207D - PS11 10-12-10 SOLUTION

# GE 207D - PS11 10-12-10 SOLUTION - GE 207D 13.1/13.2 – 3D...

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Unformatted text preview: GE 207D 13.1/13.2 – 3D Coordinate Systems & Vectors 12 October 2010 1) The points and a) About the xy-plane b) About the yz-plane c) About the y-axis d) About the origin e) About the plane f) About the point are symmetric in the sense given below. Find a, b, c. 2) Find an equation for the plane through a) Parallel to the xy-plane b) Perpendicular to the y-axis c) Parallel to the yz-plane 3) Show that center and radius. that satisfies the given conditions: is an equation for a sphere, and find the Center: 4) Find an equation for the sphere if the line segment joining and is a diameter. Center: 5) Show that the points , , and are the vertices of a right triangle. Therefore, P, Q, and R are the vertices of a right triangle with PQ as the hypotenuse. 6) There are two points and . Find the vector and determine . 7) Let a) b) c) , , and . Find the following: d) e) 8) Find the unit vector in the direction of . 9) Find the unit vector whose direction is opposite of . 10) Label the vectors. 11) A man wants to paddle his canoe across a river from a point X to the point Y on the opposite shore directly across from X. If he can paddle the canoe at the rate of 5 miles per hour, and the current in the river is 3 miles per hour, in what direction θ should he steer his canoe in order to go straight across the river? What is his resultant speed across the river? 12) A 200-pound weight is suspended by wires as shown in the following figure. Find the force exerted by each of the wires (called the tension) and determine the magnitude of each. (Hint: the resultant of the two tensions must counterbalance the weight.) The component of F1 to the left must equal the component of F2 to the right. The components of F1 and F2 pointing upwards must together equal the weight pulling down. 13) An airplane has an airspeed of 600 miles per hour. If the pilot is steering the plane in the direction N30°E and the wind is blowing from the northwest (N45°W) at the rate of 50 miles per hour, find the resultant velocity of the plane. The direction of the resultant is called the true course of the plane and the magnitude of the resultant is called the ground speed. Find the true course and ground speed of the plane. True course Ground speed (or N34.70°E) mph ...
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