100hw2

# 100hw2 - r 1 t = r 2 t may not produce all of the points...

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Math 100 Homework 1 fall 2010 due 30/9 1. (11.6, 18a) Determine whether the line x = 3 t ; y = 7 t ; z = t intersects the plane 2 x - y + z + 1 = 0 . If so, Fnd the coordinates of the intersection. 2. (11.6, 30) ±ind an equation of the plane through the points P 1 ( - 2 , 1 , 4), P 2 (1 , 0 , 4) that is perpendicular to the plane 4 x - y + 3 z = 2. 3. (11.7, 40) Identify the surface z 2 = 4 x 2 + y 2 + 8 x - 2 y + 4 z and make a rough sketch that shows its position and orientation. 4. (12.1, 44) How many revolutions will the circular helix r ( t ) = ( a cos t, a sin t, 0 . 25 t ) make in a distance of 10 units measured along the z-axis? 5. (12.1, 52) Suppose that r 1 ( t ) and r 2 ( t ) are vector-valued functions in 2- space. Explain why solving the equation
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Unformatted text preview: r 1 ( t ) = r 2 ( t ) may not produce all of the points where the graphs of these functions intersect. 6. (12.2, 50) ±ind where the tangent line to the curve r ( t ) = ( e-t , cos t, 3 sin t ) at the point (1 , 1 , 0) intersects the yz-plane. 7. (12.2, 52) Let r 1 ( t ) = (2 e-t , cos t, t 2 + 3) r 2 ( t ) = (1-t, t 2 , t 3 + 4) . Show that the graphs of r 1 ( t ) and r 2 ( t ) intersect at P = (2 , 1 , 3). ±ind the acute angle between the tangent lines to the graphs of r 1 ( t ) and r 2 ( t ) at the point P . 1...
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