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Calculus
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12 Nov 2019

Let v= i+j-k and w= 2i-j+k

a.) Compute v dot w

b.) Compute v cross w

c.) Find the angle between v and w. You may express this angle as the inverse cosine(or arccosine) of a number.

Please show your work and explain so I can understand it as well, thanks!

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Hubert Koch
Hubert KochLv2
15 Aug 2019
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Related questions

please explain or no credit, and please wrie exact answers, nodecimals!

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I need help on number 2. I can't seem to find alocal max or min let alone the absolute.
Overview: You will identify, solve, and fully analyzea "real world" optimization problem of your choosing. It should bea problem that we did not cover in class, but you are free toconsult other sources for inspiration. If you get your idea fromanother source, you should both cite it and add some originalthoughts to your write-up.
Details: What you hand in to me should consist of thefollowing parts:
(1) An introduction clearly stating theproblem to be solved, including any necessary explanation of theset-up as well as clearly defined variables, parameters, etc. Theportion should be written out in full sentences. In particular, youshould identify the quantity to optimized (i.e., maximized orminimized) and identify any constraints or boundary conditions. Thequantity being optimized should be a function of two or morevariables.
WHAT I NEED HELP ON----->(2) A translationof the story problem in part (1) to a purely mathematical problem.You should then fully solve the mathematical problem by (i) findingand classifying all critical points, (ii) analyzing the boundariesor constraints, and (iii) deciding the absolute max/min value andwhere it occurs.
(3) A brief conclusion in which you discussthe implications of the mathematics in part (2) for the originalstory problem. This portion should also be written in fullsentences.

---so far what I have done--

The pool is an open top consisting of a rectangle and a semicircle. I put a constraint on volume and set it equal to10000 m^3 . So What I am trying to figure out is whatdimensions create the lowest surface area. I found a local minat r= 7.815,w=15.631 but that means that their would be noheight for the box. does that make sense? are theirother points I should be checking?

so far I have

V=2rwh+.5pi(r^2)w

h=(V-.5pi(r^2)w)/2rw

S=4rh+2wh+pi(r)w+pi(r^2)

S=2V/w+V/r+.5w(pi)r

partials are

Sr=-V/r^2 +.5w(pi)

Sw=-2V/w^2+.5pi(r)

Srr=2V/r^3

Sww=4V/w^3

Swr=.5(pi)

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