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32_hwc1SolnsODDA - A nicer way to express this Note that...

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A nicer way to express this: Note that since d = ( d/a ) d when a = 0, - bd/a d = d a - b a . Thus, with d arbitrary, the vectors of the form - bd/a d are precisely all of the multiples of the vector - b a . Notice that the prescription all of the multiples of the vector - b a also gives us the set of vectors orthogonal to a b when a = 0 as long as b = 0. Therefore, for any vector a in IR 2 , define a = - b a . ( * ) Then, we can answer: If a = 0 , then every vector in IR 2 is orthogonal to a . Otherwise, the set of all vectors that are orthogonal to a is the set of all multiples of a . Later on, we will see that the definition ( * ) is quite useful. The symbol is called the
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