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?