Angle of Inclination of Line in Vector Equation

1. May 25, 2010

Cuisine123

1. The problem statement, all variables and given/known data
Find the angle of inclination of each of the following lines.
i) r = (2,-6) + t(3,-4) ii) r = (6,1) + t(5,1)

B) prove that the tangent of the angle of inclination is equal to the slope of the line.

2. Relevant equations
N/A

3. The attempt at a solution
I know that the angle ø, 0° < ø < 180°, that a line makes with the positive x-axis is called the angle of inclination of the line. However, I don't have any idea how to approach this question.

2. May 25, 2010

rock.freak667

Well your lines are in the xy-plane.
So why don't you draw the lines and find the angle using some trigonometry?

OR you can find the dot product with a unit vector in the direction of the x-axis <1,0>

3. May 25, 2010

Cuisine123

How do find the solution without having to draw the lines?

4. May 25, 2010

rock.freak667

the dot product of the direction of the vector line and the unit vector in the direction of the x-axis will give you the angle.