Following Through
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Following Through
Find the equation of a plane that passes through the following points:?
Find the equation of a plane that passes through the following points:
A(3, -4, -8), B(13, 0, -15), and C(-7, 5, -10).
a) Find the normal to the plane
b) Find an equation for the plane.
Define the vectors:
AB = = <13 - 3, 0 - -4, -15 - -8> = <10, 4, -7>
AC =
The normal vector n, of the plane is orthogonal to any vector that lies in the plane. Take the cross product.
n = AB X AC = <10, 4, -7> X <-10, 9, -2> = <55, 90, 130>
Any non-zero multiple of n is also a normal vector to the plane. Divide by 5.
n = <11, 18, 26>
With the normal vector to the plane and a point in the plane we can write the equation of the plane. Let's choose point A(3, -4, -8). Remember, the normal vector to the plane is orthogonal to any vector that lies in the plane. Define R(x,y,z) to be an arbitrary point in the plane. Then vector AR lies in the plane.
n • AR = 0
n •
<11, 18, 26> •
11(x - 3) + 18(y + 4) + 26(z + 
= 0
11x - 33 + 18y + 72 + 26z + 208 = 0
11x + 18y + 26z + 247 = 0
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The Follow Through - So High
Is leading a girl on without following through cheating?
Scenerio: Your boyfriend goes out and gets numbers. Calls them and ask when will they get together and what will they do when it happens. But here's the catcher he has no intention of following through but does it to stroke his ego. Is that cheating?
If he's with you and his ego still needs that much stroking, you need to find someone with fewer ego issues.
That might be the most juvenile thing I've answered about so far.
Don't put up with it. It's a big game, and sooner or later it's going to blow up.
In any case, it's inconsiderate and insensitive to you and to these other girls he's playing games with.
If he can lie to them so casually, why not you? People, in my experience, are unlikely to show respect selectively. They tend to have it for people across the board or not. The fact that he's treating these other girls in such a disrespectful way is concerning.
Be careful that you're not the one being fooled...
Filed under: Airfix Toy Soldiers
Excellent points.For me, as an artist, yes I didn’t have to go to art school to learn the skills that I needed. But I did. I could have apprenticed or taken classes at the Art Students League on the cheap, or gone to a significantly cheaper school than I did etc. But I’m lucky, I’ve always known that I’ve wanted to make art. I never had doubts about what I wanted to with my life. But that was just me. Many kids end up switching majors or not even following through on a job that they have a degree in. Because they don’t know what they want to do, but feel pressure to go on to college.Also whenever I look on job sites for art-related work, a college education is a requirement for all jobs listed. Is that right? Probably not, but I can’t starve death while the world catches up to my opinions or becomes more enlightened or prices for higher education drop.Right now my wife is getting a great education for relatively little money. Yes there are loans. Yes it is difficult. But she’ll be able to get a better job when she’s through./argumentfromemotion
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