Angle between two lines given the slopes

In this video, I showed how to find the angle between two lines given the equations or slopes

[jc.nogueira]

Hi,
I believe it would be easier just to get both slopes (m1, m2) from the equations.
Since m1=tan(alpha1) and m2=tan(alpha2), we get both angles.
Then we can calculate the angle between the slopes.

I really enjoy your channel. Greetings from Uruguay, South America.

[Dominus_Potatus]

I thought a really conplicated workings and forget about the simple working.
This is why I love your videoes, really reminds me how math is'nt supposed to be complicated.

[mattsgamingstuff]

I did it by defining unit vectors along the lines and using the dot product. a (dot) b = ab cos theta. Since I made a and b unit I just took the arccos of the dot product and it gave me an angle. It ended up being the larger angle but it was not hard to find the smaller angle since they add up to 180 degrees.

[wes]

y=mx+b where m is the slope and b is an offset. We can ignore b in each equation. For y=x/2–1, m1=1/2. For y=–x+2, m2=–1
Let u1=[1, 1/2]/(√5/2) represent a unit vector parallel to the first line.
Let u2=[1, –1]/√2 represent a unit vector parallel to the second line.
Let θ=acos(√10/10)=71.565° The symbol • represents the inner product between two vectors.

[danobro]

114 views and no comment? - let me fix that! (love your vids btw)

[holyshit]

Let l_{1} : y=a_{1}x+b_{1}
l_{2} : y = a_{2}x+b_{2}
Slope is tangent of angle between line and abscissa
a_{1} = tan(theta_{1})
a_{2} = tan(theta_{2})
Now angle between lines will be difference of angles theta_{2} and theta_{1}
so we calculate tangent of the difference of angles
and if denominator is zero we have perpendicular lines
otherwise we calculate inverse tangent (arctan)

[samarcando]

Nice exercise, but I'm worried, this kind of exercises do not explained, only mechanical processes, no analysis, thus the knowledge is limited, you make the maths so pleasant...hugs from Colombia!

[JourneyThroughMath]

Because I've never seen this type of problem before, I'll generalize a solution before I watch the video: i would find a lin perpendicular to on of the given lines at a point of my choosing. Either in this case because the slope of a perpendicular would be an integer. This gives me a right triangle. Then i find the lengths of two of the sides (this would require me knowing the intersection). Then use inverse trig to find the angle.

[Vengeance-yblm]

Could vectors be used to solve this problem too ?

[AS-ixqd]

you can simply use: theta=abs(atan(m1)-atan(m2))
in other words...
theta=abs(atan(1/2)-atan(-1))

[menh]

Can you do a video about how to draw a graph of a 2 variables equation and explain it
For example (x+2y)(x+3y+1)=2

[johnka]

Don’t you think arctan(3) would be better than tan^(-1)(3)?

[Ron_DeForest]

You are good. Just for shiggles I checked to see what the arctan of 3 was in degrees was. It’s 71.5650512. Good guess.

[junkgum]

I thought arctan m1 - arctan m2 was the fastest answer.

[nikhilprabhakar]

This was interesting. However, a derivation or proof of the formula could be better as then there won't be any confusions regarding the signs. Now, its not clear why the signs are flipped. Also, I would really appreciate few more examples and edge cases.

[waferlayout]

To draw y(_x curve y strain number, x independent variableand that is a ....

[i_want_to_be_free]

Can we just say the tan(alpha mines beta)

[golddddus]

Not good. So what is the slope of the line? By definition tg(φ)=k. φ is the angle between the straight line and positive part of the x-axis. The difference between two angles gives the angle between two straight lines. At the same time, it gives both a obtuse and a acute angle. In our case, the solution calls for a negative value. You can see from your picture that the angle in the first quadrant is obtuse. And solution is π-acctg(3).😎