Find the angle between the following pairs of line :

and

We know that angle between two lines given with their vector equation is the angle between their parallel vectors always.

By using dot product to find the angle between the lines using their parallel vectors .

= (3+2–4)+λ(+2+2)

= (5–2)+μ(3+2+6)

= 3+2–4, = +2+2

= 5–2, = 3+2+6

= = 3

= = 7

Let θ be the angle between given lines, so using the dot product,

=

= = 19

θ =