Angle of Inclination of Line in Vector Equation

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Homework Help Overview

The discussion revolves around finding the angle of inclination of lines represented in vector form, specifically in the xy-plane. The original poster seeks to understand how to determine this angle and its relationship to the slope of the line.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants suggest using trigonometry to visualize the lines or employing the dot product with a unit vector to find the angle. There are questions about how to approach the problem without drawing the lines.

Discussion Status

Participants are exploring different methods to find the angle of inclination, including drawing the lines and using trigonometric relationships or vector operations. There is no explicit consensus on a single approach, but various ideas are being discussed.

Contextual Notes

The original poster expresses uncertainty about how to begin the problem, indicating a potential lack of familiarity with the concepts involved. There are also references to the relationship between the angle of inclination and the slope of the line, which is under consideration.

Cuisine123
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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.
 
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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>
 
rock.freak667 said:
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?
 
Cuisine123 said:
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.
 

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