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Question 204887: Hi all, Im still having trouble with these vector problems, I cant solve the problems listed below for the following:
Let ~u = 3~i - ~j - 2~k and ~v = 2~i + ~j + ~k.(Again, the ~ symbols mean that there is and arrow symbol above the value in the positive direction)
I need to:
a) Find the corresponding unit vectors for ~u and ~v
b) Calculate the dot product of the angle between ~u and ~v.
Some help with steps and explanations on how to solve would be great.
Thanks, -Nick.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Let ~u = 3~i - ~j - 2~k and ~v = 2~i + ~j + ~k.(Again, the ~ symbols mean that there is and arrow symbol above the value in the positive direction)
I need to:
a) Find the corresponding unit vectors for ~u and ~v
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Find the magnitude of each.
for u: = sqrt(9 + 1 + 4) = sqrt(14)
Divide the vector by its magnitude to get the unit vector.
--> 3i/sqrt(14) - j/sqrt(14) - 2k/sqrt(14)
You can manipulate it to get the radical out of the denominators, or not.
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for v: = sqrt(4 + 1 + 1)
= sqrt(6)
Same as above.
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b) Calculate the dot product of the angle between ~u and ~v.
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It's not the dot product of the angle.
I assume you want to find the angle between the 2 vectors.
Find the dot product:
Multiply the i, j, and k elements, and add them.
u dot v = 3*2 + -1*1 + -2*1 = 6-1-2 = 3
The dot product is the product of the 2 magnitudes times the cos of the angle between them. So the cos is
dot/Mag(u)*Mag(v)
cos = 3/sqrt(14)*sqrt(6)
cos = 3/sqrt(84)
angle = 70.89 degs
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