# The angle between two lines

#### Petrus

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

Regards,
$$\displaystyle |\pi\rangle$$

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#### MarkFL

Staff member
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?

#### Petrus

##### Well-known member
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?
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,
$$\displaystyle |\pi\rangle$$

#### MarkFL

Staff member
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.

#### Petrus

##### Well-known member
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.
I solved it Thanks for the help!

Regards,
$$\displaystyle |\pi\rangle$$

Last edited: