Question: Let ~v = 1, 1 and ~u = 1, 2. (a) First, compute proj~v ~u. (b) Now find two more vectors, ~a and ~b, that

Let ~v = 1, 1 and ~u = 1, 2. (a) First, compute proj~v ~u. (b) Now find two more vectors, ~a and ~b, that have the same orthogonal projection onto ~v = 1, 1 as ~u = 1, 2. In other words, we want ~a and ~b to satisfy proj~v ~a = proj~v ~b = proj~v ~u. Hint: sketch an illustration and also work with equations on paper - use both geometric and algebraic viewpoints.

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