emathematics.net
Español
User: desconectar
 
Maths Exercices

Line-Line Angles


The angle θ between two lines is the angle between two direction vectors of the lines.
Take line r with direction vector u and line s with direction vector v, then

The angle between the two lines is defined by:


Calculate the angle between the following lines:

and

Solution:

u=(2,1,1) and v=(-1,2,1)

Therefore

θ=80.41º


To find the angle between the line

2x+3y-z+1=0
x-y+2z+2=0

and the line

3x-y+z-3=0
2x+y-3z+1=0

Solution:

u=
i j k
2 3 -1
1 -1 2
=5i-5j-5k u=(5,-5,-5)

v=
i j k
3 -1 1
2 1 -3
=2i+11j+5k v=(2,11,5)

θ=48.70º