# Thread: angle between lines

1. ## angle between lines

find the angle formed by the intersection of each pair of lines

$2x+3y-z+9=0$ and $x+2y+4=0$

so the Cartesian coordiantes must be (2,3,-1) and (1,2,0) respectively

therefore the angle between is the dot product/magnitude of line 1x magnitude of line two

so $\frac{(2(1)+3(2)-1(0)}{\sqrt14 \sqrt5}=cos^{-1}(\frac{8}{8.36})=17.02^o$

the book says $44.2^o$

2. Originally Posted by william
find the angle formed by the intersection of each pair of lines

$2x+3y-z+9=0$ and $x+2y+4=0$

so the Cartesian coordiantes must be (2,3,-1) and (1,2,0) respectively

therefore the angle between is the dot product/magnitude of line 1x magnitude of line two

so $\frac{(2(1)+3(2)-1(0)}{\sqrt14 \sqrt5}=cos^{-1}(\frac{8}{8.36})=17.02^o$

the book says $44.2^o$
can someone please verify the text book is wrong? or give me guidance

3. William, You've been around long enough to know two things:

1) Folks who can help are volunteers who wander by when they can. If you need an instant answer, you may need to pay for it in some other venue.

2) Many do not even look at posts that are already answered. When you comment on your own post, it looks answered and is much less likely to be answered by anyone else - EVER.

Perhaps the second equation should have a +2z in it?

What do you mean "cartesian coordinates"? Do you mean "direction numbers" or maybe something else?

4. Originally Posted by TKHunny
William, You've been around long enough to know two things:

1) Folks who can help are volunteers who wander by when they can. If you need an instant answer, you may need to pay for it in some other venue.

2) Many do not even look at posts that are already answered. When you comment on your own post, it looks answered and is much less likely to be answered by anyone else - EVER.

Perhaps the second equation should have a +2z in it?

What do you mean "cartesian coordinates"? Do you mean "direction numbers" or maybe something else?
yes i understand, sorry about that

also, those equations are directly from the book, i checked them over twice to make sure it is exact, and by those cartesian coordiantes i mean direction vectors

5. First, those are not lines they are planes.
The angle between two intersecting plane is the angle between the normals.
If the planes you posted are indeed correct then I agree with your answer.
But do double check.