math192_hw1sp06

# math192_hw1sp06 - HW1 Solutions 12.1 Three-Dimensional...

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Unformatted text preview: HW1 Solutions 12.1 Three-Dimensional Coordinate Systems 10. The circle x 2 + z 2 = 9 in the plane y = − 4 20. (a) x = 3 (b) y = − 1 (c) z = 2 24. (a) ( x + 3) @ + ( y − 4) 2 = 1 , z = 1, (b) ( y − 4) 2 + ( z − 1) 2 = 1 , x = − 3, (c) ( x + 3) 2 + ( z − 1) 2 = 1 , y = 4 34. 1 ≤ x 2 + y 2 + z 2 ≤ 4 50. x 2 + y 2 + z 2 − 6 y +8 z = 0 ⇒ x 2 +( y 2 − 6 y +9)+( z 2 +8 z +16) = 9+16 ⇒ ( x − 0) 2 +( y − 3) 2 +( z +4) 2 = 5 2 ⇒ the center is at (0 , 3 , − 4) and the radius is 5 50. | PA | = radicalbig (2 − 3) 2 + ( − 1 − 1) 2 + (3 − 2) 2 √ 1 + 4 + 1 = √ 6 | PA | = radicalbig (4 − 3) 2 + (3 − 1) 2 + (1 − 2) 2 √ 1 + 4 + 1 = √ 6 Thus P is equidistant from A and B 12.2 Vectors 8. (a) − 5 13 u = (big − 15 13 , 10 13 )big 12 13 v = (big − 24 13 , 60 13 )big − 5 13 u + 12 13 v = (big − 3 , 70 13 )big (b) 6421 13 12. −→ AB = < 1 , 1 >, −→ CD = < − 1 , − 1 >, −→ AB + −→ CD = < , > 16....
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## This note was uploaded on 02/05/2008 for the course MATH 1920 taught by Professor Pantano during the Spring '06 term at Cornell.

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math192_hw1sp06 - HW1 Solutions 12.1 Three-Dimensional...

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