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I have two vectors: $$ a=\begin{pmatrix} {1} & {1} & {1} \ \end{pmatrix} \\ b=\begin{pmatrix} {1} & {2} & {k} \ \end{pmatrix} $$ These vectors should be orthogonal. What is value of $k$?

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    $\begingroup$ I would recommend to post questions on mathematics here: math.stackexchange.com. This forum is focussed mainly on quantum computing but your question is concerning linear algebra. $\endgroup$ – Martin Vesely Jan 9 '20 at 16:42
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    $\begingroup$ I'm voting to close this question as off-topic because this isn't specifically relevant to quantum computing or quantum information. $\endgroup$ – Sanchayan Dutta Jan 9 '20 at 19:16
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$$ \left\langle a| b \right\rangle= \begin{pmatrix} {1} & {1} & {1} \ \end{pmatrix} \begin{pmatrix} {1} & {2} & {k} \ \end{pmatrix} $$ Since the two vectors are orthogonal,so the inner product of them is zero: $$ 0=1+2+k \\ k=-3 $$

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  • $\begingroup$ Just note that this is valid only in case so-called standard inner product. Generaly the inner product is defined as $x^{T}Ax$ where $A$ is positive matrix. Apparently $A=I$ for standard inner product. I suppose the standard product was meant in the question. $\endgroup$ – Martin Vesely Jan 9 '20 at 16:30

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