homework 1

homework 1 - 0.0. 1 Hand-in Assignment 1 Solutions (Math...

Info iconThis preview shows pages 1–3. 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: 0.0. 1 Hand-in Assignment 1 Solutions (Math 20300 DD, PP, ST) Your Name: Foster, Antony Your Student ID: 0000 (only last 4 digits) Your Instructor: Prof. A. Foster Due Date: Friday, February 8, 2008. SECTION 13.1 (pages 829834): DO Exercises 1, 3, 4, 5, 12, 18, 19, 36, 40, and 42. Formulas Used: Distance Formula in Three Dimensions : The distance k P 1 P 2 k between the points P 1 ( x 1 ,y 1 ,z 1 ) and P 2 ( x 2 ,y 2 ,z 2 ) in 3-Dimensional real space or R 3 is k P 1 P 2 k = p ( x 2- x 1 ) 2 + ( y 2- y 1 ) 2 + ( z 2- z 1 ) 2 . (1) Equation of a Sphere : An equation of a sphere with center C ( ,, ) and radius is ( x- ) 2 + ( y- ) 2 + ( z- ) 2 = 2 . (2) In particular, if the center is the origin O (0 , , 0), then an equation of the sphere is x 2 + y 2 + z 2 = 2 (3) Volume of a spherical cap : The volume V of a cap of a sphere centered at the origin O (0 , , 0) with radius and height h < of the cap (measured from the endpoint of a diameter of the sphere) is V = 1 3 h 2 (3 - h ) (can be derived using calculus) . (4) Distance from a Point to a Plane : Let P be a plane with equation ax + by + cz + d = 0 and P ( x ,y ,z ) is a point not in the plane P then the distance d ( p, P ) from the point P to the plane P is given by d ( P, P ) = | ax + by + cz + d | a 2 + b 2 + c 2 . (5) 2 0. Exercise 1 : Suppose you start at the origin, move along the x-axis a distance of 4 units in the positive direction, and then move downward a distance of 3 units. What are the coordinates of your position? Solution. Without any drawings we start at the origin O (0 , , 0) and move along the x-axis a distance of 4 units in the positive direction. This puts us at the point A (4 , , 0). From A we move downward a distance of 3 units, this puts our final position at the point B (4 , ,- 3). Note this is a point in the xz-plane. tu Exercise 3 : Which of the points P (6 , 2 , 3) , Q (- 5 ,- 1 , 4), and R (0 , 3 , 8) is closest to the xz-plane? Which point lies in the yz-plane?...
View Full Document

This note was uploaded on 05/05/2011 for the course EEE 212 taught by Professor Des during the Spring '11 term at Syracuse.

Page1 / 6

homework 1 - 0.0. 1 Hand-in Assignment 1 Solutions (Math...

This preview shows document pages 1 - 3. Sign up to view the full document.

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