Find all values of $k$ for which the angle between the vectors $\begin{pmatrix} k \\ 1 \\ 1 \end{pmatrix}$ and $\begin{pmatrix} 1 \\ k \\ 1 \end{pmatrix}$ is $\frac{\pi}{3}.$
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<|im_start|>user
Find all values of $k$ for which the angle between the vectors $\begin{pmatrix} k \\ 1 \\ 1 \end{pmatrix}$ and $\begin{pmatrix} 1 \\ k \\ 1 \end{pmatrix}$ is $\frac{\pi}{3}.$
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0,4
Find all values of $k$ for which the angle between the vectors $\begin{pmatrix} k \\ 1 \\ 1 \end{pmatrix}$ and $\begin{pmatrix} 1 \\ k \\ 1 \end{pmatrix}$ is $\frac{\pi}{3}.$
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