What value of K parameter of the following two vectors? [closed]

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 $$k$$?

• 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. – Martin Vesely Jan 9 '20 at 16:42
• I'm voting to close this question as off-topic because this isn't specifically relevant to quantum computing or quantum information. – Sanchayan Dutta Jan 9 '20 at 19:16

$$\left\langle a| b \right\rangle= \begin{pmatrix} {1} & {1} & {1} \ \end{pmatrix} \begin{pmatrix} {1} & {2} & {k} \ \end{pmatrix}$$ Since the two vectors are orthogonal,so the inner product of them is zero: $$0=1+2+k \\ k=-3$$
• 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. – Martin Vesely Jan 9 '20 at 16:30