20075ee1_1_HW1

20075ee1_1_HW1 - CHAPTER 1 1.1 Given the vectors M = − 10...

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 Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 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 , . 36 , . 14) b) the magnitude of 5 a x + N − 3 M : (5 , , 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. The three vertices of a triangle are located at A ( − 1 , 2 , 5), B ( − 4 , − 2 , − 3), and C (1 , 3 , − 2). a) Find the length of the perimeter of the triangle: Begin with AB = ( − 3 , − 4 , − 8), BC = (5 , 5 , 1), and CA = ( − 2 , − 1 , 7). Then the perimeter will be ` = | AB | + | BC | + | CA | = √ 9 + 16 + 64+ √ 25 + 25 + 1 + √ 4 + 1 + 49 = 23 . 9 . b) Find a unit vector that is directed from the midpoint of the side AB to the midpoint of side BC : The vector from the origin to the midpoint of AB is M AB = 1 2 ( A + B ) = 1 2 ( − 5 a x +2 a z ). The vector from the origin to the midpoint of BC is M BC = 1 2 ( B + C ) = 1 2 ( − 3 a x + a y − 5 a z ). The vector from midpoint to midpoint is now M AB − M BC = 1 2 ( − 2 a x − a y + 7 a z ). The unit vector is therefore a MM = M AB − M BC | M AB − M BC | = ( − 2 a x − a y + 7 a z ) 7 . 35 = − . 27 a x − . 14 a y + 0 . 95 a z where factors of 1 / 2 have cancelled....
View Full Document

{[ snackBarMessage ]}

Page1 / 3

20075ee1_1_HW1 - CHAPTER 1 1.1 Given the vectors M = − 10...

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