# 16 5 pts the equation z 3 r 2 cos 2 θ is in

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_________________________________________________________________ 16. (5 pts.) The equation z = 3 r 2 cos 2 ( θ ) is in cylindrical coordinates. Obtain an equivalent equation in terms of rectangular coordinates (x,y,z).

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TEST1/MAC2313 Page 5 of 5 _________________________________________________________________ 17. (5 pts.) The point (5,-5 3,10) is in rectangular coordinates. Convert this to spherical coordinates ( ρ , θ , φ ). ( ρ , θ , φ ) = . _________________________________________________________________ 18. (5 pts.) Do the lines defined by the equations <x,y,z> = <3,1,2> + t<2,-1,-2> and <x,y,z> = <10,8,-5> + t<1,3,-1> intersect? If they do intersect, what is the point of intersection?? _________________________________________________________________ 19. (5 pts.) What is the area of the triangle in three space with vertices at P = (1, 0, 0), Q = (0, 2, 0), and R = (0 , 0, 3). _________________________________________________________________ 20. (5 pts.) Do the three 2-space sketches of the traces in each of the coordinate planes of the surface defined by y = 1 - x 2 - z 2 . Work below and label carefully. Then attempt to do a 3 - space sketch in the plane of the surface on the back of page 4.
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