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Cell["\<\
Go through this entire notebook. Answer all the questions posed.
On the You Try It, you MUST insert your own NEW values or functions.
Print out your results and attach to a 1-page summary of what you learned \
from this lab.\
\>", "Subsubtitle"],

Cell[CellGroupData[{

Cell["Getting Started in Plotting Lines and Planes in 3D", "Title"],

Cell[TextData[StyleBox["Chapter 10, Sections 3 ",
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Cell["Introduction", "Section"],

Cell[TextData[{
  "OBJECTIVE: To learn to use ",
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  " to plot lines and planes"
}], "Text"],

Cell[TextData[{
  "In this module, you will learn how ",
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  " can help you plot the lines and planes you have been reading about. In \
the process of plotting lines and planes, you will gain insight into their \
vector definitions."
}], "Text"],

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Cell["Technology Guidelines", "Subsection",
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Input cells within a given notebook.\nSAVING NOTEBOOKS\n\tYou can save \
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Cell["Lines and Planes", "Section"],

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Cell[TextData[StyleBox["Interpreting Lines Using Their Vector Definition",
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Cell["\<\
You can construct straight lines in two and three dimensions using the vector \
definition. Given two points on the line, we will first determine the \
direction of the line and then write any other point on the line as the \
position vector to that point plus a multiple (t) of the vector in the \
direction of the line.  We will start with two points, finding the direction \
determined by those two points, and then writing and plotting the parametric \
equations for the line in three dimensions.\
\>", "Text"],

Cell["", "Text"],

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Cell[TextData[StyleBox["Constructing Planes Using Vectors",
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Cell[TextData[{
  "We begin by constructing a plane from three points on the plane. We use \
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    p3 = {\(-4\), 0, 9}; \n
    Print["\<{x,y,z} = \>", 
      pts = Simplify[\((p1 - origin)\) + s\ \((p2 - p1)\) + t\ \((p3 - p2)\)]]
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Cell[TextData[{
  "We can also find the equation of the plane using the cross product to find \
the normal vector to the plane. Then we can find the points",
  Cell[BoxData[
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      sol\[LeftDoubleBracket]1, 1, 2\[RightDoubleBracket], {x, \(-10\), 10}, {
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  " are exactly the same in both parametric and nonparametric form."
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Cell["You Try It", "Section"],

Cell[CellGroupData[{

Cell["Finding equations of lines", "Subsection"],

Cell["\<\
To find the equations of lines and planes, just change the numbers in the \
points given, then re-execute the commands to see other lines. You can \
replace the red items in the following input commands to create a new line.\
\>", "Text"],

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        RowBox[{"{", 
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Cell["Finding equations of planes", "Subsection"],

Cell["\<\
Now, pick any 3 points, replace the red numbers with your points, and execute \
the cell to see the plane determined by the three points.\
\>", "Text"],

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        pts = Simplify[
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  \(vec1 = p2 - p1; \nvec2 = p3 - p2; \nnormal = Cross[vec1, vec2]\), 
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  \(Plot3D[sol\[LeftDoubleBracket]1, 1, 2\[RightDoubleBracket], {x, \(-10\), 
        10}, {y, \(-10\), 10}, AxesLabel -> {"\<x\>", "\<y\>", "\<z\>"}]; 
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*******************************************************************)