11.2 – Vectors in Space
May 15th, 2011 by corricelli
Hello,
Please use this page to discuss Chapter 11, Section 2.
Learn by playing… Check out this link: http://www.intmath.com/vectors/7-vectors-in-3d-space.php.
Happy blogging,
Mrs. Corricelli
12 Responses to “11.2 – Vectors in Space”
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For number 39 and 41 on tonights homework I understand how to find out if they are parallel but how do you find out if they are orthoganol are not. Do you do the dot product or something?
Well Srinath, for number 39 it’s parallel because two nonzero vectors u and v are parallel if there is some scalar c such that u = cv. In this case, c = -1.5. For number 41, you can go back to chapter 6.4 page 461 and you can see that orthogonal vectors only exist when the dot product of vectors u and v equals 0. So, number 41 is neither orthogonal nor parallel.
Two vectors are orthogonal if their dot product equals zero.
Do dot products have any applications other than determining angles between vectors?
I was just looking through the book evan to see and im not too sure because the only time i see the dot product is in finding angles, so i look to the next couple sections and i saw something alot like it, the cross product, in 11.3 so maybe its just the basic formula then were going to build off of it later.
For some clarification on parallel vectors, the scalar can be any number, as long as it works for all three coordinates, correct?
As far as I’ve seen the scalar can be any constant number that is being “distributed” into the the three coordinates of the vector, thus scaling the vector to become longer or shorter on the plane.
Hey,
today in period 7 some people were asking about graphing the rose petal in 3D.
I found a website that you can graph a polar function in 3D.
http://graph.seriesmathstudy.com/
and this is a link to help you get there because you have to change around some of the settings to graph it
http://www.seriesmathstudy.com/polargraph.htm
DJ, yes the scalar can be any number, 1, -1, 2/3, basically anything, odd/even, negative/positive…
***** ^ the 1, -1, 2/3 are just examples of three random scalars; don’t mean to confuse anyone! sorry!
Does anyone have like a list of like vector orthogonality properties or something?, im confused as to what an orthogonal vector is and what it means as far as math equations go….
Steve, I know I’m probably late….but atleast in time before the finals!
Well, two vectors are orthogonal, or perpendicular basically, when the angle between them is 90 degrees. To check if two vectors (make sure they’re both in component form) are orthogonal, their dot product has to be 0. I hope this helps…