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GATE EC 2023 Set 1 — Question 11

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MCQ+1 / -0.33MediumVectors & Vector OperationsLinear AlgebraEngineering Mathematics

Engineering Mathematics → Linear Algebra → Vectors & Vector Operations

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Question

Let v1=[120]\mathbf{v}_1 = \begin{bmatrix} 1 \\ 2 \\ 0 \end{bmatrix} and v2=[213]\mathbf{v}_2 = \begin{bmatrix} 2 \\ 1 \\ 3 \end{bmatrix} be two vectors. The value of the coefficient α\alpha in the expression v1=αv2+e\mathbf{v}_1 = \alpha \mathbf{v}_2 + \mathbf{e}, which minimizes the length of the error vector e\mathbf{e}, is
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