How do you find the scalar and vector projections of b onto a given #a = ‹3, 2, 1›#, #b = ‹0, 1, 3›#?

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Answer 1 · 2015-11-21T12:51:51

#proj_a(b) = (0, 1/2, 3/2)#

#proj_a (b) = v = lambda b#

#v + n = a Rightarrow n = a - lambda b#

#n cdot b = 0#

#(a - lambda b) cdot b = 0#

#a cdot b = lambda b cdot b#

#lambda = (a * b)/(b * b) = (0 + 2 + 3)/(0 + 1 + 9) = 5/10 = 1/2#

#v = 1/2 b = (0, 1/2, 3/2)#