Angle Between Two Planes

[@starlight200816]

Finally a math video on youtube that doesn't take 30 minutes to explain one concept.

[@MathDoctorBob]

@antodez1234 You're welcome! There are two equivalent equations of the plane we use: ax+by+cz=d and a(x-x0) + b(y-y0) + c(z-z0) = 0. The second one is better: it says take all vectors perpendicular to the vector (a,b,c) and based at the point (x0,y0,z0). If we consider the angle between two planes, we are allowed to shift to parallel planes to get the same angle. If you shift both planes so they contain the origin, they now have equation in the form ax + by + cz = 0. Hope it helps. - Bob

[@MathDoctorBob]

You're welcome! You should think of the dot product as generalizing length of a vector. If we dot a vector with itself, we sum the squares of the components. In general, the dot product measures how much the vectors point in the same "direction," and it does that by comparing components (by multiplying). Think of R itself. If we multiply two one-vectors (numbers), a positive result means they have the same sign (direction), and negative means opposite. This also captures lengths.

[@MathDoctorBob]

@jimmykim808 You're welcome! Thanks for the comment. - Bob

[@cjracer1000]

Thank you, sir. Much respect.

[@aNuthaRedneck]

Here's a problem/calculation I can't wrap my mind around. I am building an all metal house. The roofs have a slope of 4:12 and intersect at 90 degrees. I need to have a metal pan bent to fit in the valley of this intersection. What is the angle the metal valley should be bent? How does one calculate that angle? Or, what formula is used to calculate that angle?

[@rugbyrocks123321]

Great video!!

[@mtb1392]

Very helpful video. Thank you.

[@MathDoctorBob]

Yes. If you draw the picture, you'll note that the only change is the direction of one normal vector by -1 or 180 degrees.

[@cnthach]

awesome! explained it so much better than my professor =)!

[@dominicholloman7337]

Thank you!

[@mominahussain5552]

Respect, amazing drawings.

[@MathDoctorBob]

@moosemooseson You're welcome! - Bob

[@MathDoctorBob]

Your welcome, and good luck on finals!

[@erinkelley7047]

thanks so much that was very helpful!

[@BarnabasJK]

Thanks a lot sir!

[@alexandgarciacalle]

GreaVideo! thank you. But maybe I dont understand, why do you add the final products of the dot product if they are of different components? (i,j,k) Thank you again.

[@MathDoctorBob]

Thanks!

[@virginialikesyou]

Thank you very much!!! Very helpful to meee!!

[@luizpaganelli_]

Do we ignore the constants because the planes can be shifted anywhere and the acute angle upon intersection would still be the same?

[@MathDoctorBob]

Constants will change the normal vectors by the same constant, which then cancels itself out in the cosine formula.

[@maerybatus4166]

very well done. thanks!

[@MathDoctorBob]

@virginialikesyou You're welcome! - Bob

[@jjmini27]

Brilliant, thank you!

[@girl18296]

What if we arrive at cos aplha= -0.5. We'll get the angle to be 120 degrees. But the question asks to find the 'acute' angle between the plane. What do I do now? Simply 180-120=60 ??

[@MRAXELGRINDER]

Awesome

[@tonyminglu]

so buff lol

[@haydn2097]

chad explains how to find the angle between two planes

[@MathDoctorBob]

Tough call. Bullied until about the 8th grade, but wife is totally a Stacy.

[@gothveggies]

Thank you!!

[@moosemooseson]

thanks bob!

[@MathDoctorBob]

That's the idea. Here's what I get. First use cos(O) = (u,v)/|u||v| = -88/sqrt(115.168) =-.633109909. arccos gives the angle between 0 and pi, so O'=2.256360618 rad = 129.28 degrees. Going acute gives O=180-O'=51 degrees.

[@MathDoctorBob]

You're welcome!

[@sirrobinthebrave1]

good vid, but what's with the staff of wisdom?

[@OverTheBuilding]

thanks!

[@needsum12love]

Sir can u teach me if the answer is more than 90 degree, how should i know i should take the answer minus 90 or using 180- the ans.

[@DontReadThisAgain]

As far as I know, you take 180 - (answer). There are two angle you can get, one obtuse and one acute, unless they are perpendicular. So both angles will always add up to 180. If you get the obtuse, then subtracting 180 by the obtuse angle will give you the acute angle on the other side. Have a nice day!

[@jabased]

i fuckin thank you :')