math192_hw1sp06

math192_hw1sp06 - HW1 Solutions 12.1 Three-Dimensional...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

This note was uploaded on 02/05/2008 for the course MATH 1920 taught by Professor Pantano during the Spring '06 term at Cornell.

Page1 / 2

math192_hw1sp06 - HW1 Solutions 12.1 Three-Dimensional...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online