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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
 #1
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The answers are plane, plane, plane, line.

 Mar 3, 2020

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