Linear Algebra and Its Applications · Problem 3.4.2

Orthogonality — Gilbert Strang

Mathematics · projection-orthonormal-vectors

Problem

Project b=(0,3,0)b = (0, 3, 0) onto each of the orthonormal vectors a1=(23,23,−13)a_1 = (\frac{2}{3}, \frac{2}{3}, -\frac{1}{3}) and a2=(−13,23,23)a_2 = (-\frac{1}{3}, \frac{2}{3}, \frac{2}{3}), and then find its projection pp onto the plane of a1a_1 and a2a_2.

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