If two lines do not intersect, can they be perpendicular?
I need to evaluate if two lines are perpendicular and give a reason for my answer.
So: To show that the lines are not perpendicular, I need to show by the dot product method that my calculation does not = 0. Because cos(0)=90, perpendicular lines.
I have two lines below:
I need to start with my components in (i, j, k) form.
The angle between the lines is the angle between their directions. The directions are U and V.
r1=j+ak +λ(2i+4j-3k)
r2=4i+3j-6k+μ(i+5j+k)
u=2i+4j-3k,
v=i+5j+k,
u.v=(2, 4, -3)(1, 5, 1)=(2+20-3)=19
Is this enough or do I need to go further, i.e
|u|=√2+4+3=3
|v|=√2+20+3=5
cosθ=u.v/|u|.|v|
19/15=1.267
θ=but when I inverse cos I get a mathematical error when I try to inverse cos this figure?
ahh shoot! That was dumb. sorry
its not:
|u|=√2+4+3=3
|v|=√2+20+3=5
but
|u|=√2²+4²+3²=√29
|v|=√2²+20²+3²=√413
cosθ=u.v/|u|.|v|
19/√29.√413=1.17
θ=80°
Therefore the lines are not perpendicular.
Please excuse the dumb error.