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Sections 1.2 solutions

Sections 1.2 solutions - Sec 1.2...

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Sec. 1.2 3,4,5,6,8,9,11,12,16,17,21,23 3. v u U v uU ± 1 5 u 3,4 U and w u U w u U ± 1 10 u 8,6 U give unit vectors in the directions of v u , w u Then cos u ± v u ± w u U v uUU w u U ± v u U v ± w u U w u U ± 1 5 u U ± 1 10 u U ± 48 50 ± 24 25 , and u ± cos u 1 24 25 ± 0.28379 (in radians) Given w u ± u U the vectors u 4,3 U , u u U , u u 4, u 3 U make an angle of 0 U , 90 U , 180 U , respectively, with w u . 4. a) v u ± u u v u U ± u u v u ± v u U ± u U v 2 ± u 1 b) Expand, the cross-terms cancel: u v u ² w u U ± u v u u w u U ± v u ± v u u w u ± w u ± 0 (the diagonals of a rhombus meet at right angles) c) u v u ² 2 w u U ± u v u u 2 w u U ± 1 u 4 ± u 3 5. ū 1 ± 1 10 u 3,1 U , ū 2 ± 1 3 u 2,1,2 U Ū 1 ± u u 1,3 U and Ū 2 ± u 1, u 2,0 U or u 0, u 2,1 U are perpendicular to ū 1 and ū 2 respectively. Note that any combination c u 1, u U ² d u 0, u U is perpendicular to ū 2 and that exhausts all the possibilities. 6. a) Any multiple of u 1,2 U is perpendicular to u 2, u 1 U .
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