Find the coordinates of the point of intersection and the angle of the intersection

[katejackson]

Show that the following lines intersect. Find the coordinates of the point of intersection and the angle of intersection.

L1: x=7+2t and L2: x=-3+3s

y=4+t y=4-s

 

[Deleted member 4993]

Show that the following lines intersect. Find the coordinates of the point of intersection and the angle of intersection.

L1: x=7+2t and L2: x=-3+3s

y=4+t y=4-s

What are your thoughts?

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[pka]

Show that the following lines intersect. Find the coordinates of the point of intersection and the angle of intersection
L1: x=7+2t and L2: x=-3+3s
y=4+t y=4-s

Solve this system: \(\displaystyle \begin{align*}7+2t &=-3+3s\\ 4+t &= 4-s \end{align*}\)
That gives the point of intersection.
Find \(\displaystyle D_1~\&~D_2 \) the two direction vectors of these lines.

Then the acute angle formed by these lines is \(\displaystyle \arccos\left(\dfrac{|D_1\cdot D_2|}{\|D_1\|~\|D_2\|}\right) \)