MHB How Do You Calculate the Angle Between Two Lines?

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SUMMARY

The discussion focuses on calculating the angle between two lines represented by the equations $$x+2y-3=0$$ and $$-3x+y+1=0$$. Participants confirm that the normal vectors of these lines are $$(1,2)$$ and $$(-3,1)$$, respectively. The correct method to find the angle involves using the dot product of the normal vectors and applying the inverse cosine function. The conversation also suggests that this topic may be more appropriate for the Pre-Calculus forum.

PREREQUISITES
  • Understanding of normal vectors in linear equations
  • Knowledge of the dot product of vectors
  • Familiarity with the inverse cosine function
  • Basic concepts of angles between lines in a Cartesian plane
NEXT STEPS
  • Study the properties of normal vectors in linear algebra
  • Learn about the dot product and its geometric interpretation
  • Explore the inverse cosine function and its applications in trigonometry
  • Research methods for finding angles between lines in coordinate geometry
USEFUL FOR

Students and educators in mathematics, particularly those studying geometry and linear algebra, as well as anyone seeking to understand the relationship between lines in a Cartesian coordinate system.

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Decide the angle between line $$x+2y-3=0$$ and $$-3x+y+1=0$$ we use ON-cordinate
progress
I know that their normalvector is $$(1,2)$$ and $$(-3,1)$$ but what shall I do next?
Is this correctly understand
33paq7r.png

Regards,
$$|\pi\rangle$$
 
Last edited:
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Re: the angle between two line

Don't you have two forms for the dot product, one involving the components and one involving the angle between them?
 
Re: the angle between two line

MarkFL said:
Don't you have two forms for the dot product, one involving the components and one involving the angle between them?
My picture did not work:S That is what I did, I just wounder if I can use the normal vector, cause normal vector got same slope if I understand correctly

Regards,
$$|\pi\rangle$$
 
Re: The angle between two line

If two vectors are normal (if I understand you to mean orthogonal or perpendicular) then their dot product will be zero. What you did was correct, you just need to solve for the angle using the inverse cosine function.

edit: Unless you are to use some other method to find the angle subtending the lines, this topic should actually be in the Pre-Calculus forum. I'll wait until I know for sure before moving it.
 
Re: The angle between two line

MarkFL said:
If two vectors are normal (if I understand you to mean orthogonal or perpendicular) then their dot product will be zero. What you did was correct, you just need to solve for the angle using the inverse cosine function.

edit: Unless you are to use some other method to find the angle subtending the lines, this topic should actually be in the Pre-Calculus forum. I'll wait until I know for sure before moving it.
I solved it :) Thanks for the help!:)

Regards,
$$|\pi\rangle$$
 
Last edited:

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