Cross product homework

  • #1
1. Find the sine of the angle between and .

NV_vp.jpg




2. AxB = ABsin(alpha)



3. I know T = (3,1,0) and U = (2,4,0), and I calculated that V = TxU = (0,0,10), so the magnitude of V is 10.

Then I did 10 = sqrt(10)*sqrt(20)*sin(alpha)

Divided 10 by sqrt(10)*sqrt(20), took the inverse sine, and obtained 45 degrees, which is incorrect.
 

Answers and Replies

  • #2
Mentallic
Homework Helper
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I haven't studied 3-D vectors, but this problem can be simplified into a 2-D diagram, and quite easily since z=0 for both vectors.
I also got the answer of 45o by answering it with trigonometry.

But the question does say find the sine of the angle, correct? So are we looking for the answer [itex]1/\sqrt{2}[/itex] ?
 
  • #3
We are not finding sine(theta), we are finding theta, which is what I calculated.
 
  • #4
HallsofIvy
Science Advisor
Homework Helper
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You have already been told that 45 degrees ([itex]\pi/4[/itex] radians) is the correct answer. What makes you say it is incorrect?

As a check, use the fact that [itex]\vec{u}\cdot\vec{v}= |\vec{u}||\vec{v}|cos(\theta)[/itex]. Since, here, [itex]|\vec{u}\times\vec{v}|= \vec{u}\cdot\vec{v}[/itex], [itex]sin(\theta)= cos(\theta)[/itex] and the angle, being in the first quadrant must be [itex]\pi/4[/itex].
 

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