Calc 3 Exam 1 Sin 2011

Calc 3 Exam 1 Sin 2011 - MAC2313 Exam 1 Dr Sin No...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
MAC2313 Exam 1 Dr Sin No Calculators. Answer the questions in the spaces provided on the question sheets. Please write your answers in full detail. If you run out of room for an answer, continue on the back of the page or on other paper. Name: 1. (7 points) Sketch the surface give by x 2 + y 2 - z 2 = 4 . (Start by sketching some traces (intersections with planes) and use them to help you see the 3-D picture.) Solution: Figure 1: z = 0 trace
Background image of page 1

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

View Full DocumentRight Arrow Icon
MAC2313 Exam 1 Dr Sin Figure 2: x = 0 trace ( y = 0 trace looks the same) Figure 3: 3D picture
Background image of page 2
MAC2313 Exam 1 Dr Sin 2. (8 points) (a) (4 points) Find the angle between the planes 5 x - y - 2 z = 1 and 4 x + y + z = 6. (You may leave your answer in terms of inverse trig functions.) Solution: We can take n 1 = h 5 , - 1 , - 2 i and n 2 = h 4 , 1 , 1 i as normal vectors of the planes. Then if θ is the angle between the planes, we have cos θ = n 1 · n 2 | n 1 || n 2 | = 17 30 18 . so
Background image of page 3

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

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 10/20/2011 for the course MAC 2313 taught by Professor Keeran during the Spring '08 term at University of Florida.

Page1 / 4

Calc 3 Exam 1 Sin 2011 - MAC2313 Exam 1 Dr Sin No...

This preview shows document pages 1 - 4. Sign up to view the full document.

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