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# Consider the following sets of points:

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Consider the following sets of points:

\begin{align*} &S_1 \text{ is the set of all points (x, y, z) such that x+y + 2z = 1}, \\ &S_2 \text{ is the set of all points Q such that }\overrightarrow{OQ} = \begin{pmatrix}1 \\ 2\\ 3 \end{pmatrix} + s \begin{pmatrix} 1 \\ 1 \\ 2 \end{pmatrix} + t \begin{pmatrix} 2 \\ 2 \\ 4 \end{pmatrix} \text{for some real s and t},\\ &S_3 \text{ is the set of all points (x, y, z) such that x = y = 2z}, \\ &S_4 \text{ is the set of all points Q such that }\overrightarrow{OQ} = \begin{pmatrix}1 \\ 2\\ 3 \end{pmatrix} + s \begin{pmatrix} 1 \\ 1 \\ 2 \end{pmatrix} + t \begin{pmatrix} 2 \\ 2 \\ 3 \end{pmatrix} \text{for some real s and t}. \end{align*}

Each of these sets of points is either a line or a plane. For each set above, enter "line" if it's a line, and "plane" if it's a plane. Enter the answers in the order they appear in the list above.

Could someone help me? I thought it was plane, plane, line, line, but it's wrong.

Mar 2, 2020