Finding Equation of a Plane

What you are looking for is Matrix equation of a plane.

However, you can also take the long way around and solve this through using simple algebra. Think about solving parallel equations, and substitution.

Good luck on your studies!

(x-2)/3 = (y-1)/2 = (1-z)/4 is the line passing through the point (2,1,1) and having the direction ratios (3,2,4).

-x/2 =3-y = (z-3)/2 is the line passing through (0,3,3) with direction ratios of (2,1,2).

Have you studied direction ratios? Look in your notes/text/handouts.

There are probably several ways to proceed.

You can find 3 points in the plane. You have (2,-1,3). If you set the numerators in the line equations to zero (0=0=0), that gives you two more points (a,b,c), and (d,e,f).

Now you have 3 points from which you can make 2 vectors in the plane originating at any one of the three points. Cross these vectors to get a vector, P, perpendicular to the plane.

Now the plane consists of all points (x,y,z) through the chosen intersection point (a,b,c). So any vector (x-a)i + (y-b)j + (z-c)k dot P = equals zero (because they are perpendicular to P).

L = (1/2) d v² s CL

• L = Lift, which must equal the airplane's weight in pounds
• d = density of the air. This will change due to altitude.
• v = velocity of an aircraft expressed in feet per second
• s = the wing area of an aircraft in square feet
• CL = Coefficient of lift

https://www.grc.nasa.gov/www/k-12/WindTunnel/Activities/lift_formula.html

Homework alert

I'm giving you a GA for that. Everyone else is showing that they are knowledgeable and intelligent by answering the question although most are showing some restraint.

The best way the OP will learn from here is if everyone holds out from answering OP. With such an ambiguous question, OP needs to truthfully answer other questions first (but here, I know that that only happens about 15 - 20% of the time).

Or maybe OPs don't deserve that kind of help, and everyone else that reads the posts can be edified. Hard to screen newcomers to an anonymous forum. Hmmm.

Well, that's my post! Anybody else feel like I do?

OK - you got me. The "ambiguous" I was thinking about another post. I have had a long day and probably need to go to bed.