1. [V] Let P be the plane through the point (2, 0, 3) that is perpendicular to the line with parameterization r(t) = (1 + 3t)i + (2 − t)i + 4tk. Find a level set equation and two different parameterizations for P. 3. [V] Find the three intercepts of the plane 3x +y + 2z = 12 and use them to sketch the plane. How would you work out the area of the triangle in the plane that is formed by these three intercepts? (Don’t do the calculation: Just explain.)

4. [V] Find a parametrization of the plane that contains both the point (2, 4, 6) and the line x = 7 − 3t, y = 3 + 4t, z = 5 + 2t.

the answer   is 200

step-by-step explanation:

this is a problem about poisson probabilities.   i don't know if you've

already studied poisson distributions, or if you have a place to look

to read more about the subject.  

here's how you can see a poisson distribution coming.   when there are

a lot of events that may happen at any time (or any place), and when

you're counting how many of them happen at a particular time (or a

particular place), and each event is independent of the others, then

the result is a poisson distribution.   this is roughly true for the

chocolate chips; one chip being in a cookie has only a small effect on

the probability that another chip will be in the cookie.

once you know you have a poisson distribution, you know a lot.   there

is only one parameter to a poisson distribution, so if you know the

mean, you know everything.   the form of the distribution is

  probability of n chips = {[e^(-x)]*(x^n)} / (n! )

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