MATH311ansHW2

MATH311ansHW2 - Math 311 Homework 2 partial answers and...

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Unformatted text preview: Math 311, Homework 2 partial answers and solutions 1.4.8. Answer: (a) 13 . (b) √ 11 and √ 17 . (c) arccos 13 √ 181 ≈ . 26 radians. 1.4.15. Since | v | = √ 1 + 9 + 4 = √ 14 , the unit vector in the direction v is n = 1 √ 14 , 3 √ 14 ,- 2 √ 14 . Thus (a) x · n = 2- 9- 2 √ 14 =- 9 √ 14 , (b) the component of x in the direction v is p = ( x · n ) n =- 9 14 ,- 27 14 , 9 7 , and the perpendicular component is x- p = 37 14 ,- 15 14 ,- 2 7 . 1.4.18. Answer: the lengths are √ 22 , √ 70 , and √ 58 . All the angles are acute. 1.4.21. e i = (0 , , . . . , , 1 , , . . . , 0) , where the only 1 appears in the i ’th position. So for i 6 = j , e i · e j = 0 · 0 + 0 · 0 + . . . + 1 · 0 + . . . + 0 · 1 + . . . · 0 = 0 . On the other hand, for i = j , e i · e i = 0 · 0 + 0 · 0 + . . . + 1 · 1 + . . . + 0 · 0 = 1 . 1.4.23. Since 4 i + 3 k has length 5 , the unit vector perpendicular to the panels is 4 5 i + 3 5 k . Similarly, the unit vector in the direction of the sun is...
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MATH311ansHW2 - Math 311 Homework 2 partial answers and...

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