anonymous
  • anonymous
Could somebody explain how to do this: Find the angle between the given vectors to the nearest tenth of a degree. u = <-5, -4>, v = <-4, -3> Answer choices: A. -9.1 Degrees B. 1.8 Degrees C. 0.9 Degrees D. 11.8 Degrees Not sure how to find an angle between vectors.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anikhalder
  • anikhalder
Do you know how to find the magnitude or length of a vector? And also so you know about scalar or dot product of 2 vectors?
anonymous
  • anonymous
I know Scalar and Dot Product. @anikhalder I sort of know magnitude...
anikhalder
  • anikhalder
That's perfect! So let's go through this: What is the length of u vector?

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anonymous
  • anonymous
I'm not sure how to solve for length...
anikhalder
  • anikhalder
so its like, suppose i have a vector a = <3, 4> Then the length of the vector a is : \[\left| a \right|=\sqrt{3^{2} + {4^{2}}}\] \[\left| a \right|=\sqrt{25}\] That is the length of vector a is 5 So using the same way can you solve for the length of vector u?
anonymous
  • anonymous
Oh! Is the magnitude |u| = SqRt. 41 ?
anikhalder
  • anikhalder
Perfect! You rock! What about the magnitude (or length) of vector v?
anonymous
  • anonymous
|v| = 5 ?
anikhalder
  • anikhalder
Awesome! Now do you know the formula for dot (or scalar) product of 2 vectors a and b?
anonymous
  • anonymous
Yes, would the product be: a x b = 32 ?
anikhalder
  • anikhalder
Yes that's correct! But, I will suggest when writing dot product don't use 'x' sign. You will learn that there is another type of product called the vector or cross product which uses this sign...but we don't need to worry about right now. Suppose I have a vector a and vector b Then the dot product of vectors a and b is also defined as: \[a.b=\left| a \right|\left| b \right|\cos \theta\] Where theta is the angle between the vectors a and b. So for our question at hand. Let's replace a by u and b by v. So, we get: \[u.v=\left| u\right|\left| v\right|\cos \theta\] We can replace u.v as 32 and the magnitudes of u and v on the right hand side of the equation to get: \[\cos \theta=\frac{ u.v }{ \left| u \right|\left| v \right|}\] Can you solve for costheta now?
anonymous
  • anonymous
Is costheta = .99 ?
anonymous
  • anonymous
@anikhalder
anikhalder
  • anikhalder
Yes! I find so as well. Now just find the cosine inverse of 0.99 and you'll get it in degrees
anonymous
  • anonymous
I got 8.1 degrees, approximately, but that is not one of my answers.
anikhalder
  • anikhalder
That's what I get and now I must confess that I am confused as well
anikhalder
  • anikhalder
Let's verify
anonymous
  • anonymous
Ok
anikhalder
  • anikhalder
http://onlinemschool.com/math/assistance/vector/angl/ Can you type the values in and see what you get for costheta because I get 0.99 in this website as well
anonymous
  • anonymous
I am getting .99
anonymous
  • anonymous
@anikhalder Can you help me with another problem, and then maybe go back to this one?
anikhalder
  • anikhalder
oh wait
anonymous
  • anonymous
Express the complex number in trigonometric form. -3 + 3 square root of three i
anikhalder
  • anikhalder
http://www.rapidtables.com/calc/math/Arccos_Calculator.htm
anonymous
  • anonymous
And I'm confused as to what that calculator meant.
anikhalder
  • anikhalder
Check this, we were just using 0.99, we cant do that we have to use the full result which was 0.9995120761 plug this and find the cos inverse. You will see that we get our answer :)
anonymous
  • anonymous
Oh. I see. So the answer would be 1.8 degrees?
anikhalder
  • anikhalder
Yep! And yes just take 4 minutes and see this video on complex numbers! he explains better than me :)))
anonymous
  • anonymous
What video?
anikhalder
  • anikhalder
Sorry...my bad i forgot to give the link: https://www.youtube.com/watch?v=6z6fzPXUbSQ
anonymous
  • anonymous
Thank you so much. (: I watched that video, though, and am still confused on my example. He helped me with a couple others, but the one I posted about is a bit confusing after watching the video.
anikhalder
  • anikhalder
You mean its like : \[3+3\sqrt{3}i\] So, \[\left| z \right| = \sqrt{3^{2}+(3\sqrt{3})^{2}} = 6\] and \[\tan \theta = \frac{ 3\sqrt{3} }{ 3}\] i.e. \[\theta = 60 degrees\] Now, in polar or trigonometric form, z = \[\left| z \right|(\cos \theta + i \sin \theta)\] Just substitute the values and find the answer :)))
anonymous
  • anonymous
What is the Z value?
anonymous
  • anonymous
And is the theta value 120 degrees?
anikhalder
  • anikhalder
you can say \[\left| z \right|\] is like the absolute value of the complex number (like the|dw:1437768487456:dw|
anonymous
  • anonymous
So the z value is 3SqRt3. But you have in 3 as positive, the 3 is negative. So would that make the equation (in radians): 3SqRt2(Cos2pi/3 + i sin2pi/3)
anikhalder
  • anikhalder
oho...i forgot the minus sign...yep!
anonymous
  • anonymous
Ok, so the theta value is 120 degrees? Not 150?
anikhalder
  • anikhalder
Wait hold on, how is r coming to 3sqrt3 it should be 6
anonymous
  • anonymous
Oh. Ok, how do you get 6?
anikhalder
  • anikhalder
|dw:1437768935393:dw|
anonymous
  • anonymous
Oh ok thanks. So it would be the same answer, but 6 as r vs. 3sqrt3 as r?
anikhalder
  • anikhalder
yes it would 6(costheta + i sintheta)
anonymous
  • anonymous
Ok thanks! Theta = 2pi/3 right?
anikhalder
  • anikhalder
yes. because tantheta in this case is 3sqrt3 / -3 which will give theta as 2pi/3
anikhalder
  • anikhalder
:) I guess so. Please verify the answer with your book and your teacher. If I made any mistake please tell me :)))
anonymous
  • anonymous
Thanks so much!
anikhalder
  • anikhalder
Thank you very much for bearing with me! My pleasure! Have a nice night! I will go to sleep!

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