week02 - Math 23 Sections 110-113 B. Dodson Week 2...

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Math 23 Sections 110-113 B. Dodson Week 2 Homework: 12.2 vectors: unit, standard unit, notations 12.3 dot product: orthogonal, proj, comp 12.4 cross product: formula, properties Problem 12.2.25: Find a unit vector ±u that has the same direction as ±a = 8 ± i - ± j + 4 ± k. [variation/continuation: find a vector of length 4 in the opposite direction.] Solution: The length | 8 ± i - ± j + 4 ± k | = 64 + 1 + 16 = 81 = 9 , so the unit vector is ±u = 1 | ±a | ±a = 1 9 8 ± i - ± j + 4 ± k · = 8 9 ± i - 1 9 ± j + 4 9 ± k. Likewise, the vector with length 4 is - 4 9 8 ± i - ± j + 4 ± k · .
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2 Problem 12.3.23bc: Determine whether the given vectors are othogonal, parallel or neither. (b) ±a = < 4 , 6 >, ± b = < - 3 , 2 > . (c) ±a = - ± i + 2 ± j + 5 ± k, ± b = 3 ± i + 4 ± j - ± k. Solution: (b) Recall that vectors are parallel if one is a scalar multiple of the other, ±a = c ± b, for a scalar c. This says < 4 , 6 > = c < - 3 , 2 > = < - 3 c, 2 c >, so 4 = - 3 c,
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week02 - Math 23 Sections 110-113 B. Dodson Week 2...

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