Angle of Inclination of Line in Vector Equation

[Cuisine123]

Homework Statement

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.

Homework Equations

N/A

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.

 

[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>

 

[Cuisine123]

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>

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

 

[rock.freak667]

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

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.