ma100_hw1

ma100_hw1 - ,-3 , 51 > . 20. (a) 3 v = 3(-2 i +...

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Homework answer 1 Sec 12.1 24. (a) We can project the right circular cylinder on the xz-plane since the graph does not depend on y. Then, we can easily get the equation of circle in xz-plane ( x - a ) 2 + ( z - a ) 2 = a 2 . It is exactly the equation of the right circular cylinder. Similarly, (b). ( x - a ) 2 + ( y - a ) 2 = a 2 . (c). ( y - a ) 2 + ( z - a ) 2 = a 2 . 40. AP = 2 BP p ( x - 1) 2 + ( y - ( - 2)) 2 + ( z - 0) 2 = 2 p ( x - 0) 2 + ( y - 1) 2 + ( z - 1) 2 x 2 + y 2 + z 2 + 2 3 x - 4 y - 8 3 z + 1 = 0 ( x + 1 3 ) 2 + ( y - 2) 2 + ( z - 4 3 ) 2 = 44 9 since 44 9 > 0, the set of points P is on the sphere with centre ( - 1 3 , 2 , 4 3 ) and radius r 44 9 . Sec 12.2 12. ( a ) u - w = < 2 , - 1 , 3 > - < 1 , 1 , 3 > = < 1 , - 2 , 0 > . (d) 3( u - 7 v ) = 3( < 2 , - 1 , 3 > - 7 < 4 , 0 , - 2 > ) = < - 78
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Unformatted text preview: ,-3 , 51 &gt; . 20. (a) 3 v = 3(-2 i + 3 j ) =-6 i + 9 j . (b) k v k = p (-3) 2 + 4 2 + 1 2 = √ 26 .-2 v k v k =-2 √ 26 (-3 i + 4 j + k ) . 39. (a) the set of all points on the sphere with centre (0 , , 0) and radius 1. (b) the set of all points inside the closed sphere with centre (0 , , 0) and radius 1. (c) the set of all points outside the closed sphere with centre (0 , , 0) and radius 1. 1...
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