I am trying to show that the angle between two straight lines is given by:
I am using vector methods but my problem is the algebra. If the vector equation of a line is given by . And the second line by subscript 2, the angle between the lines is given by:
for a straight line of the form y = mx + c we have:
So, the angle between the two lines is given by
At this stage I decided to square both sides and look for a chance to combine 1 and to give then simplify and take a square root to get back to
instead things got very messy indeed. Am I on the right track? I know it's murder trying to type lots of algebra but I suspect there would be less algebra if it was done right! A few lines in the right direction would be greatly appreciated!
Thanks again, HallsofIvy!
I tried it your way and it works fine. The problem I am having is that I don't always go the right way, particularly with algebra!
This is what I did and as you can see it rapidly gets out of hand even though I am not making any mistakes!
and as you can see I have this hanging term and no clear way to get to the required solution. Have I made a mistake and if not can you see how to get my final line into the answer we know and love?