2300hw1SP11 - aircraft intercept. As shown below, ship A is...

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——————————————————————————————————– MATH 2300 - Calculus III Spring 2011 Homework 1 - DUE Wednesday, February 2 ——————————————————————————————————– 1. Find the equation of the sphere centered at (3 , - 1 , - 2), which is tangent to: (a) the yz -plane (b) the plane y = 7 2. Consider the parallelogram shown below, with vertices at A (2 , - 1 , 4), B (1 , 0 , - 1), C (1 , 2 , 3), and D . Find the following: (a) the coordinates of D (b) the interior angle at B (in degrees) (c) a vector of length 8 in the direction of # » AC (d) proj # » BC # » BD (e) the area of the parallelogram (f) the equation of the plane containing the parallelogram 3. Let a = i - 2 j +3 k , b = 4 i - j +2 k , and c = 2 i - 3 k . Find the value of x such that a + x b is orthogonal to c . 4. Given the lines: L 1 : x = 4 t - 1 , y = t + 3 , z = 2 t + 7 and L 2 : x = 12 s - 13 , y = 6 s + 1 , z = 3 s Find the parametric equations of the line which is orthogonal to both L 1 and L 2 , and passes through their point of intersection. 5. Two surface ships on maneuvers are trying to determine a submarine’s course and speed to prepare for an
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Unformatted text preview: aircraft intercept. As shown below, ship A is located at (4, 0, 0), whereas ship B is located at (0, 5, 0). All coordinates are given in thousands of feet. Ship A locates the submarine in the direction of the vector 2 i +3 j-1 3 k , and ship B locates it in the direction of the vector 18 i-6 j-k . Four minutes ago, the submarine was located at p 2 ,-1 ,-1 3 P . The aircraft is due in 20 min. Assuming that the submarine moves in a straight line at a constant speed, to what position should the surface ships direct the aircraft? 6. Find the equation of the plane containing the point (2 ,-4 ,-5) that satises each condition: (a) Parallel to the xz-plane. (b) Perpendicular to the line x = t-1 , y = 2 t + 3 , z = 4 + t . (c) Containing the line x = t-1 , y = 2 t + 3 , z = 4 + t ....
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