- #1
Kernul
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- 7
Homework Statement
The problem asks me to evaluate the angle between these two lines:
##r : \begin{cases}
x - 2y - 3 = 0 \\
3y + z = 0
\end{cases} s : \begin{cases}
x = 1 + 4t \\
y = 2 - 3t \\
z = 3
\end{cases}##
both oriented to the decreasing ##y##.
Homework Equations
The Attempt at a Solution
Having found ##\vec v_r = (-2, -1, 3)##, ##\vec v_s = (4, -3, 0)##, ##P_r (1, -1, 3)##, and ##P_s (1, 2, 3)##
I already know that the lines are askew. I then found out that in order to find the angle between the two lines, I have to first find a plane containing one of the two lines(for example ##r##) that is at the same time parallel to the other one(in this example ##s##). In a few words I have to find a line parallel to ##s## that meets the line ##r## in a point that belongs to ##r##.
The thing is that I don't know how to find that parallel line to ##s## that at the same time passes into a point ##P_r## belonging to the line ##r##.
Should I take one of the Cartesian equations of ##r## and see the projection of ##s## on it so to have the parallel line? And then see the interjection between this parallel line and ##r##? Or I should proceed in another way?
By the way, this is the Cartesian form of the ##s## line I found:
##s : \begin{cases}
\frac{3}{4}x + y - \frac{11}{4} = 0 \\
z - 3 = 0
\end{cases}##