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Norm after imposing orthogonality

EasyLinear Algebra~3m

The vectors a=(2,1,2)a = (2, 1, 2) and b=(1,t,2)b = (1, t, 2) are orthogonal. For that value of tt, what is the length ∥b∥\lVert b\rVert? (to 4 decimals)

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  1. Orthogonal means a⋅b=0a\cdot b = 0; solve 6+t=06 + t = 0 for tt.
  2. Then ∥b∥=1+36+4=41\lVert b\rVert = \sqrt{1 + 36 + 4} = \sqrt{41}.

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6.4031 (± 0.001)

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Asked at: Multi-Strategy Quant, Data-Driven Research

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