11.4 – Lines and Planes in Space
May 15th, 2011 by corricelli
Hello,
Please use this page to discuss Chapter 11, Section 4.
PDF File Overview: http://www.mathcs.citadel.edu/~chenm/231.dir/02fal.dir/lect10_5.pdf
Good overview site: http://www.mecca.org/~halfacre/MATH/linesandplanesinspace.htm
Happy blogging,
Mrs. Corricelli
Well i have been doing some research as i was trying to look for an interactive website that could help me see the planes as i was plotting them( to get a better angle than i was able to get by graphing it on paper) but i have not yet found one, but i did stumble across a website that i personally found to help with explaining some parts of the chapter to me that were confusing, and i hope this helps with anyone else who has questions. i will still continue to look for a useful interactive website but here is the link to the website that has helped me so much: http://www.math.hmc.edu/calculus/tutorials/linesplanesvectors/
I’m not sure where exactly to post for Chapter 11 Review, so I’ll just post here….while doing the review, I have 2 Questions; will we be required to know a question like number 45?
Secondly, for number 47 and 49….is the answer generally supposed to be in the same format as the question? Meaning in number 49, would I be wrong if i wrote instead of the answer written, 4i + 2j – 7k….
Can any one help me with question number 65 and 66? Although the answer key is provided, I don’t really understand the first step for both problems….
Also, will there be questions on volume (like number 57, 58) , and how to verify parallelograms (Q # 55, 56)?
I have a quick question about example 1 on page 832. For the part where it says “because a,b,c, are all nonzero, a set of symmetric equations is…..” if one of those HAPPENED to be zero, then would the entire equation not work, or just that section of the equation where a, b, or c equaled zero?
Ryan, I think that a part of the section of the equation would just equal zero, but someone correct me if I’m wrong.
Also, Matt that website helped so much! Thanks a lot, and I’m looking for more sites now that may be helpful.
can someone help with #33 in 11.4?
I thought i understood it, but i don’t and calc chat isnt really helping :O
thanks!
They give you two points, so you can make a vectors in component form with that, =
Then, calcchat gives another vector, , which is perpendicular to the yz plane, making it parallel to whatever plane we are looking for.
then find the cross product of these two vectors, which comes out to be
Take the dot product of this and , and you get y-z+2=0
Hope that helped!
Sorry, the computer removed all my vectors. Her’s what i meant to say. All items in parentheses are actually vectors.
They give you two points, so you can make a vectors in component form with that, (-1-0,-2-2,0-4)=(-1,-4,-4)
Then, calcchat gives another vector, (1,0,0), which is perpendicular to the yz plane, making it parallel to whatever plane we are looking for.
then find the cross product of these two vectors, which comes out to be (0,-4,4)
Take the dot product of this and (x-0,y-2,z-4), and you get y-z+2=0
Hope that helped!
Number 65
Alright I was confused about this one when I first did it too but I firgure it out and I hope this helps…
So you know that the plane is parallel to the xy plane, which means z could be any number. However you need a normal vector to find the equation of a plane. From that you know that the normal vector is (0,0,1) because that is the standard form of any plane parallel to the xy plane. From there you use the point your given (5,3,2) to find the equation.
0(x-5)+0(y-3)+1(z-2)=0
z-2=0
I hope that helps!
Ms. Corricelli, is there a secion where we can post questions about our Final Review? I wanted to ask if there will be a formula sheet provided on the test? If yes, what will it include? Thanks.
Yup – so sorry!
Just click here: http://blog.whps.org/corricelli/unit-2/final-exam-review/
Happy reviewing,
Mrs. Corricelli