HW 3 - Math E-21a Fall 2009 HW#3 problems Problems to turn...

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Math E-21a – Fall 2009 – HW #3 problems Problems to turn in on Thurs, Sept 24 : Section 9.6 : 11. Sketch the graph of the function ( , ) 6 3 2 f x y x y . 12. Sketch the graph of the function ( , ) cos f x y x . 34. Find an equation for the surface consisting of all points P for which the distance from P to the x -axis is twice the distance from P to the yz -plane. Identify the surface. Chapter 9 Review Exercises : 8. Show that if a , b , and c are in R 3 (also denoted V 3 in the text) then 2 ( ) [( ) ( )] [ ( )] a b b c c a a b c . 10. Given the points A (1, 0, 1), B (2, 3, 0), C (–1, 1, 4), and D (0, 3, 2), find the volume of the parallelepiped with adjacent edges AB , AC , and AD . 26. Find the distance from the origin to the line 1 , 2 , 1 2 x t y t z t    . 36. Identify and sketch the graph of the surface 2 2 2 1 y z x . Include several traces (cross-sections) in your sketch. Section 10.1 : In problems 6-8, sketch the curve with the given vector equation. Indicate with an arrow the direction in which t increases. 6. 3 2 ( ) , t t t r 7. ( ) ,cos2 ,sin 2 t t t t r 8. ( ) 1 ,3 , t t t t r 38. Two particles travel along the space curves 2 3 1 2 ( ) , , ( ) 1 2 ,1 6 ,1 14 t t t t t t t t
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