chap1 - www.usmanahmad.cjb.net CHAPTER 1 1.1. Given the...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
CHAPTER 1 1.1. Given the vectors M =− 10 a x + 4 a y 8 a z and N = 8 a x + 7 a y 2 a z , find: a) a unit vector in the direction of M + 2 N . M + 2 N = 10 a x 4 a y + 8 a z + 16 a x + 14 a y 4 a z = ( 26 , 10 , 4 ) Thus a = ( 26 , 10 , 4 ) | ( 26 , 10 , 4 ) | = ( 0 . 92 , 0 . 36 , 0 . 14 ) b) the magnitude of 5 a x + N 3 M : ( 5 , 0 , 0 ) + ( 8 , 7 , 2 ) ( 30 , 12 , 24 ) = ( 43 , 5 , 22 ) , and | ( 43 , 5 , 22 ) |= 48 . 6 . c) | M || 2 N | ( M + N ) : | ( 10 , 4 , 8 ) || ( 16 , 14 , 4 ) | ( 2 , 11 , 10 ) = ( 13 . 4 )( 21 . 6 )( 2 , 11 , 10 ) = ( 580 . 5 , 3193 , 2902 ) 1.2. Given three points, A( 4 , 3 , 2 ) , B( 2 , 0 , 5 ) , and C( 7 , 2 , 1 ) : a) Specify the vector A extending from the origin to the point A . A = ( 4 , 3 , 2 ) = 4 a x + 3 a y + 2 a z b) Give a unit vector extending from the origin to the midpoint of line AB . The vector from the origin to the midpoint is given by M = ( 1 / 2 )( A + B ) = ( 1 / 2 )( 4 2 , 3 + 0 , 2 + 5 ) = ( 1 , 1 . 5 , 3 . 5 ) The unit vector will be m = ( 1 , 1 . 5 , 3 . 5 ) | ( 1 , 1 . 5 , 3 . 5 ) | = ( 0 . 25 , 0 . 38 , 0 . 89 ) c) Calculate the length of the perimeter of triangle ABC : Begin with AB = ( 6 , 3 , 3 ) , BC = ( 9 , 2 , 4 ) , CA = ( 3 , 5 , 1 ) . Then | AB |+| BC |+| CA |= 7 . 35 + 10 . 05 + 5 . 91 = 23 . 32 1.3. The vector from the origin to the point A is given as ( 6 , 2 , 4 ) , and the unit vector directed from the origin toward point B is ( 2 , 2 , 1 )/ 3. If points A and B are ten units apart, find the coordinates of point B . With A = ( 6 , 2 , 4 ) and B = 1 3 B( 2 , 2 , 1 ) , we use the fact that | B A |= 10, or | ( 6 2 3 B) a x ( 2 2 3 B) a y ( 4 + 1 3 B) a z |= 10 Expanding, obtain 36 8 B + 4 9 B 2 + 4 8 3 B + 4 9 B 2 + 16 + 8 3 B + 1 9 B 2 = 100 or B 2 8 B 44 = 0. Thus B = 8 ± 64 176 2 = 11 . 75 (taking positive option) and so B = 2 3 ( 11 . 75 ) a x 2 3 ( 11 . 75 ) a y + 1 3 ( 11 . 75 ) a z = 7 . 83 a x 7 . 83 a y + 3 . 92 a z 1
Background image of page 1

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

View Full DocumentRight Arrow Icon
1.4. given points A( 8 , 5 , 4 ) and B( 2 , 3 , 2 ) , find: a) the distance from A to B . | B A |=| ( 10 , 8 , 2 ) |= 12 . 96 b) a unit vector directed from A towards B . This is found through a AB = B A | B A | = ( 0 . 77 , 0 . 62 , 0 . 15 ) c) a unit vector directed from the origin to the midpoint of the line AB . a 0 M = ( A + B )/ 2 | ( A + B )/ 2 | = ( 3 , 1 , 3 ) 19 = ( 0 . 69 , 0 . 23 , 0 . 69 ) d) the coordinates of the point on the line connecting A to B at which the line intersects the plane z = 3. Note that the midpoint, ( 3 , 1 , 3 ) , as determined from part c happens to have z coordinate of 3. This is the point we are looking for. 1.5. A vector field is specified as
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 08/12/2010 for the course ECE ECE 302 taught by Professor Ferguson during the Spring '10 term at Cal Poly Pomona.

Page1 / 13

chap1 - www.usmanahmad.cjb.net CHAPTER 1 1.1. Given the...

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