Lecture Notes 8/27/18 through 8/31/18 (complete)

Lecture Notes 8/27/18

Lecture Notes 8/29/18

Lecture Notes 8/31/18

10.2#2

Good afternoon Dr. Taylor,

I have a question regarding Problem 2 on the Section 10.2 homework. The question asks me to find a 3D unit vector in the same direction as the 3D vector a = <5,2,-1>. I went through the motions for finding a unit vector (first finding the length with the Pythagorean theorem, then dividing each vector component by the length) and got 0.913i+0.365j-0.183k as my unit vector in the same direction. I double checked the length to make sure it was 1 by doing Pythag again, and the length was 1. However, WeBWorK is saying that I'm wrong, and after a bit of Googling to find similar problems, it looks like I have done the work correctly. My question is, why am I wrong?

Thank you, and sorry if this email is a little long-winded for a single question.

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No apologies necessary, you did exactly what you should do.  It looks to me like you have the right answer, so I'm not sure what the problem with webwork is. There is a little button down at the bottom of the page that says "Email Instructor"; if you click on that it will send me a copy of your webwork page and I can usually spot  what is going wrong.

10.3#7

Dr. Taylor, I have been racking my brain for 30 minutes on this problem, and I don't see any possible answer other than the one I have given. I used the projection formula we learned in class and even went through the problem with a fellow classmate who agreed that my work seemed correct. Thank you for your time.

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well, you have the vector projection correct.  The scalar projection is b.a^  =  b.a/||a|| which is 
             [(-1)x3 + 4x(-3) + (-1)x(-4)]/√(3^2 + (-3)^2 + (-4)^2)  = [-11]/√34

So, your issue is you're using b.a/||a||^2 (and maybe also that you didn't look at the textbook?)

10.2#3

I am not sure what the problem is looking for I found the components to the unit vector in the opposite direction but I am trying to find an angle. I am just unclear on what it is asking.

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well, it's asking basically for just what you've given it: 
1) a vector point in the opposite direction from <4,4>--it will have two equal components that will both be negative, and 
2) a unit vector, that is a vector for which the squares of the components add up to 1.

Lecture Notes 8/20/18 through 8/24/18 (completed)

Lecture Notes 8/20/18

Lecture Notes 8/22/18

Lecture Notes 8/24/18

Due date for section 10.1 postponed for 24 hours

Due to the number of questions about section 10.1 hw, I've pushed the due date back to tomorrow night.

Want to make some money?

So maybe practice some calculus?

(reproduced with permission https://licensing.andrewsmcmeel.com/classroom-usage)