\magnification 2000
\parskip 10pt
\parindent 0pt
\voffset -0.4truein

\def\R{{\bf R}}
\def\C{{\bf C}}
\def\x{{\bf x}}
\def\y{{\bf y}}
\def\e{{\bf e}}
\def\i{{\bf i}}
\def\j{{\bf j}}
\def\k{{\bf k}}
\def\ep{\epsilon}
\def\f{\vskip 10pt}
\def\u{\vskip -8pt}

HW  (due this Friday) 1.2: 25, 26, 29, 34, 36, 38;
1.3: 8, 10, 14, 17, 20, 25, 28;
1.4: 4, 10, 12, 13, 17, 19, 25; 
1.5:  3, 8, 9, 15, 20

Find an equation of the line containing the point {\bf p} and is parallel to the vector {\bf a}

\f\f\f\f

Find an equation of the plane containing the point {\bf p} and containing the vectors {\bf a} and {\bf b}

\f\f\f\f\f

Find the equation of the plane containing the points (1, 2, 3), (5, 4, 7), (0, 0, 6).


\vfill
\eject


Normal form:

Find the equation of the plane containing the point {\bf p} and orthogonal to the vector {\bf n}

\vfill

Find the equation of the plane containing the points (1, 2, 3), (5, 4, 7), (0, 0, 6).

\vfill
\vfill

\eject
${\bf n} \cdot [({\bf x} - {\bf p})] = 0$

$(n_1, n_2, n_3) \cdot [(x_1, x_2, x_3) - (p_1, p_2, p_3)] = 0$

$(n_1, n_2, n_3) \cdot (x_1 - p_1, x_2 - p_2, x_3 - p_3) = 0$

$n_1(x_1 - p_1) + n_2(x_2 - p_2) + n_3(x_3 - p_3) = 0$

$n_1x_1 + n_2x_2  + n_3x_3  = n_1p_1 + n_2p_2 + n_3p_3$


Equation of a plane in $R^3$ in normal form:  $$Ax + By + Cz = D$$

\f\f\f\f
\vfill

Equation of plane in other form ${\bf x} = s{\bf a} + t{\bf b} + {\bf p}$

\f\f\f\f\f\f\
\vfill

\eject
Find the intersection of the planes $x - 2y + 5z = 0$ and $3x + 4y = 0$


\vfill

Find the distance between the point (1, 2, 3) and the line ${\bf x} = t(4, 2, 5) + (0, 6, 2)$



\end