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I am having difficulty with this problem.

Consider the sphere S of radius 5 centred at (1, 0,2). Find the equation of the plane tangent to S at the point (5,3,2).

Hint: To get started, draw this situation in 2D with a circle.
I am having difficulty with this problem.

Since the sphere and the circles center are both a z=2, the third dimension can be dropped for a moment.  Find the equation of a tangent line to the circle (x-1)^2 + y^2 = 5^2 at (5,3).

To find a perpendicular to the line going from (1,0) to (5,3), note that the size is (5-1,3-0) =
(4,3).  Flip the x and y values and negate one of them.  This gives (3,-4) or (-3,4).  Note that one of those is the negative of the other.  This is done because the dot product of (a,b)(-b,a) is -ab + ab = 0.  This means the lines are perpendicular since the dot product is 0.

The equation of the line would be 3x - 4y = 3*5 - 4*3 = 3.
That is, it is 3x - 4y = 3.

Getting back to 3 dimensional, let z be any value with 3x - 4y = 3.
This will generate a plane that is straight up and down crossing through the horizontal x-y plane.

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Scott A Wilson


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?


Experience in the area; I have tutored people in the above areas of mathematics for over two years in 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.

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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.

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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.

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