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**Unformatted text preview: **13.2b. Suppose a = -1 , 1 , 2 and b = 2 ,-1 ,-1 . Sketch each of the following quantities. (a) a + 4 j (b) 2 a-3 b 13.3a. Suppose u and v are vectors. We dene orth u v to be the difference v-proj u v . (a) Show that v = proj u v + orth u v . (b) Show that proj u v is orthogonal to orth u v . (c) Compute and sketch the vectors proj u v and orth u v for u = 2 , 5 , 7 and v = 1 , 5 , 8 . 13.3b. Compute the three angles, correct to the nearest tenth of a radian, of the triangle with vertices (1 , 2 , 3) , (3 , 5 ,-1) , and (-2 ,-3 ,-4) . List your answers from least to greatest. 13.4b. Suppose a = -1 , 3 ,-2 and b = 2 ,-1 ,-1 . Compute a b . Sketch a , b , and a b . 13.4c. Find two unit vectors orthogonal to 1 , 2 , 4 . Can you nd others? 1 For example, you may wish to do a bit of research in a library....

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