(a) Find an example of vectors a + 0, b # c so that a b...

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(a) Find an example of vectors a + 0, b # c so that a b = a c. Your example can be explicit, or you can give a clearly labeled sketch with a clear explanation. (b) Find an example of vectors a + 0, b c so that a x b a x c. Your example should be an explicit one. (c) Show that for a 0, if a · b = a ·c and a x b = a x c, then b = c. (Hint: What can you say about the relation between a and (b - c)?) Where do you need the fact that a + 0? (a) Find an example of vectors a + 0, b # c so that a b = a c. Your example can be explicit, or you can give a clearly labeled sketch with a clear explanation. (b) Find an example of vectors a + 0, b c so that a x b a x c. Your example should be an explicit one. (c) Show that for a 0, if a · b = a ·c and a x b = a x c, then b = c. (Hint: What can you say about the relation between a and (b - c)?) Where do you need the fact that a + 0?