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# hmwk2 - 13.5c Find the equation of the line consisting of...

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Math 215 Homework Set 2: §§ 13.4 – 13.5, § 13.7 Winter 2008 Most of the following problems are modified versions of homework problems from your text book Multivariable Calculus by James Stewart. 13.4a. Prove the law of cosines. (Hint: Follow the same rules as when you proved the Pythagorean theo- rem.) 13.4d. Find two unit vectors which are orthogonal to both - 3 , 1 , 5 and 2 , 3 , 5 . Can you find any others? 13.4e. Problem 43 of § 13.4 of Stewart’s Multivariable Calculus . Think carefully about how should one define the distance from P to L . 13.5a. Problem 73 of § 13.5 of Stewart’s Multivariable Calculus . One approach to this problem is to find a line perpendicular to both planes and then measure the length of that part of the line that lies between the two planes. 13.5b. Suppose P is the plane described by the equation ax + by + cz + d = 0 . Given two points ( x 0 , y 0 , z 0 ) and ( x 1 , y 1 , z 1 ) , how does one go about determining whether or not the two points lie on the same side of the plane. Carefully explain your reasoning.
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Unformatted text preview: 13.5c. Find the equation of the line consisting of those points which are equidistant from the three points (1 , 1 ,-3) , (2 , 4 ,-1) , and (-3 , 1 ,-1) . 13.7a. A solid lies above the cone z = y 7( x 2 + y 2 ) and inside the sphere x 2 + y 2 + z 2 = 8 z . Using spherical coordinates, write a description of the solid. 13.7b. Sketch the solid or surface described by the following equations and inequalities. (a) / 3 , 5 (b) z-r 2 = 0 (c) 4- sin = 0 (d) r 2 z 2-r 2 (e) 2-5 =-6 (f) / 4 3 / 4 , z r 5 (g) = / 3 . 14.1a. Problems 19-24 of 14.1 of Stewarts Multivariable Calculus . 14.1b. Find parametric equations which describe the curve dened by intersecting the cylinder r = 7 with the paraboloid of revolution 7 z + ( x 2 + y 2 ) = 0 . Sketch the two surfaces and the curve of intersection....
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