We find the distance between points and other objects.

Work in groups of 3–4, writing your answers on a separate sheet of paper.

1 Vector valued functions

point and line

point and planes

2 Normal vectors

Consider the following line: Find a vector normal to this line. Explain your reasoning.
Now consider the line \(ax+by = c\) in \(\R ^2\). Find a vector normal to this line. Explain your reasoning.
Consider the equation:
\[ \vec {n}\dotp (\vec {x}-\vec {p}) = 0 \]
Explain how this connects to finding normal vectors to lines in \(\R ^2\) of the form:
\[ ax + by = c \]
In particular, you should explain what \(\vec {n}\), \(\vec {x}\), and \(\vec {p}\) represent.
Quick! Tell me normal vectors for the following lines:
(a)
\(-3x+7y=11\)
(b)
\(4y =8\)
(c)
\(x=y\)
(d)
\(y=-4x+1\)

points and lines

points and planes