# 16 5 pts the equation r 4cos θ 10sin θ is that of a

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______________________________________________________________________ 16. (5 pts.) The equation r 4cos( θ ) 10sin( θ ) is that of a cylinder in cylindrical coordinates. Obtain an equivalent equation in terms of rectangular coordinates (x,y,z). Provide a vector equation for the straight line that is the axis of symmetry.

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TEST1/MAC2313 Page 5 of 5 ______________________________________________________________________ 17. (5 pts.) The point (-3,-4,-5) is in rectangular coordinates. Convert this to spherical coordinates ( ρ , θ , φ ). [Inverse trig fun?] ( ρ , θ , φ ) = . ______________________________________________________________________ 18. (5 pts.) Do the lines defined by the equations <x,y,z> = <0,1,2> + t<4,-2,2> and <x,y,z> = <1,1,-1> + t<1,-1,4> intersect? Justify your answer, for yes or no does not suffice. ______________________________________________________________________ 19. (5 pts.) What is the area of the triangle in three space with vertices at P = (-3, 0, 0), Q = (0, 4, 0), and R = (0 , 0, 4). ______________________________________________________________________ 20. (5 pts.) Do the three 2-space sketches of the traces in each of the coordinate planes of the surface defined by . z 1 x 2 9 y 2 4 Do not attempt to do a 3 - space sketch. If you don’t have enough space below, say where any additional work is.
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