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Question
I am having difficulty figuring out this problem. I know that for part a) the values of the variables are the ones that are displayed in the equation of a plane but I am having difficulty with the other two letters. Any help would be greatly appreciated.

What conditions on a, b, c, d will ensure that the plane pi : ax + by + cz = d has each of the following properties?
Write your answers as equations involving only the variables a, b, c, d.

(a)   pi is the plane 2x -3y = 1.
(b) pi is orthogonal to the plane x + 5y - 9z = 3.
(c) pi is perpendicular to the line L : (x, y, z) = (1, 4, 2)+ < 2, 3,-1 > t.

(a) This means the plane must have c = 0 with 2a - 3b = 1, so a = (1+3b)/2.(a) In order for the

(b) For two planes to be perpendicular, this means that the line of intersection needs to found.
Once this has been done, a vector in the plane that is orthogonal to the line needs to be found.
Once this vector has been found in each plane, the vectors need to be orthogonal to each other.

To be orthogonal to each other, the two vectors need to have a dot product that is 0.

(c) This means the plane has to pass through the point (1,4,2).
It must be of the form 2ax + 3ay - az = 12 for some value a.

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#### Scott A Wilson

##### Expertise

I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can also say that I broke 5 minutes for a mile, which is over 12 mph, but is that relevant?

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Experience in the area; I have tutored people in the above areas of mathematics for over two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree back in 1984. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

Publications
My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

Education/Credentials
Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

Awards and Honors
I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

Past/Present Clients
My clients have been students at OSU, people who live nearby, friends with math questions, and several people every day on the PC. I would guess that you are probably going to be one more.