MATB24H3 Lecture Notes - Orthogonal Complement, Dot Product, Proa
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We will call the component parallel to the vector a the orthogonal projection of b on a and denote it by projab. Let p = projab, then we want to nd p and v = such that v is orthogonal to a and b = p + v. In a23 we have shown that p = projab = ||a||2 a let us remind ourselves of the proof: Suppose that b = p + v where p = ka and v is orthogonal to a. A = (p + v) a = p a + v a = (ka) a + 0 = k(a a) Thus and and v = b p k = Example: find p, the orthogonal projection of b = [3, 1, 7] on a = [1, 0, 5] and v, the vector component of b orthogonal to a. solution. If p is the orthogonal projection of b on a, then: p = projab =
