What is the Angle Between Two Vectors?

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SUMMARY

The discussion centers on calculating the angle between two vectors, specifically v1 = (6, 3, -2) and v2 = (-2, lambda, -4), using the equation v . w = ||v|| ||w|| cos θ. The user initially calculated lambda as 8/3 but found it incorrect when compared to the expected result of 21. The conversation highlights the importance of correctly applying algebraic principles and checking calculations, particularly when dealing with fractions and radicals.

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  • Understanding of vector mathematics and dot product
  • Familiarity with trigonometric functions, specifically arccosine
  • Basic algebra skills, including manipulation of equations and fractions
  • Knowledge of vector norms and their calculations
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  • Review vector dot product calculations in detail
  • Study the properties of trigonometric functions, focusing on arccos
  • Practice solving equations involving radicals and fractions
  • Explore vector geometry and its applications in physics
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This discussion is beneficial for students studying linear algebra, particularly those tackling vector calculations and trigonometry, as well as educators looking for insights into common student misconceptions in these areas.

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Homework Statement



http://www.flickr.com/photos/coolamasta/4563408911/


Homework Equations



v . w = ||v|| ||w|| cos q

The Attempt at a Solution



i calculate until i got the lambda value is 8/3. then i compare it with 21 and the answer is wrong. i don't know what to do. please help. tq.
 
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coolamasta said:
http://www.flickr.com/photos/coolamasta/4563408911/
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Please post the question here, without pictures.
 
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The angle between two vectors v1 = (6,3,-2) and v2 = (-2,lambda,-4) is arccos (4/21). Find the value(s) of lambda. i hope u can understand the questions. thanks in advance.
 
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http://1.bp.blogspot.com/_2w6xphCWyPE/S9ntDt8niJI/AAAAAAAAAE8/6KISjbB_YCU/s1600/soalan1.jpg

http://4.bp.blogspot.com/_2w6xphCWyPE/S9ntPNm08TI/AAAAAAAAAFE/8w4Fsfu8ISA/s1600/soalan3.jpg

my lecturer gave me this assignments 3 days ago. i spent 2 days already tried to solving it but still can't solve it. i manage to solve 3 out of 5 of his questions but the other two i cant. i went to see him this morning n he's not giving me any tips or solution at all.. i tried to find example questions in his tutorial books but did not find anywhere near this questions. please help me. thanks in advance.
 
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coolamasta said:
i calculate until i got the lambda value is 8/3. then i compare it with 21 and the answer is wrong. i don't know what to do. please help. tq.
FIrst off, please do learn to use proper English. Sentences start with a capital letter. So does "I".'tq' is not a word. Stop with the silly txtspeak.

OK, had to get that off my chest.

Now as far as your calculated lambda value, show some work. It's a bit hard to figure out where you went wrong when you didn't show us what you did.
 
Sorry for that. This is my work so far.

http://2.bp.blogspot.com/_2w6xphCWyPE/S9n0ILgCiXI/AAAAAAAAAFU/W1NtWNirRBc/s1600/IMG00296-20100430-0459.jpg
 
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Correction post first:

The problem statement has v1=(6,3,-2). You stated v1=(6,3,2) in post #3. I edited post #3 to reflect the statement.
 
If \theta = \arccos(4/21), what is \cos \theta?
 
Is it there where i went wrong?
 
  • #10
Never mind, I see that you get that.

What you did wrong was to assume that your work meant that

4=-12 + 3\lambda +8

and the same for the denominator.

Look at it this way: 3/6=1/2. certainly neither of 3=1 nor 6=2 is true. Now let's put a variable in there: x/6=1/2. What is x? The solution is found by multiplying both sides by 6, yielding x=6/2=3.

In this problem you have a radical, so at some point it might help to square both sides.

A problem can arise when you do this. Just because you have a solution to the squared expression does not mean you have a solution to the original expression. For example, -1=1 is obviously false, but squaring both sides yields 1=1, obviously true. You will need to double-check your solutions.
 
  • #11
This is the only solution that i know. I've asked everyone around me and they told me they also couldn't find the answer for it. What should I do now?
 
  • #12
What you did was wrong back in elementary school days when you had to learn fractions.

What is the first step often used to solve a problem involving fractions? You want to change the problem to one not involving fractions.
 
  • #13
I think i get it now. I'll try it again. Thank you.
 
  • #14
Good luck! Let us know if you run into problems.
 

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