Find Torque About Any Line: How to Calculate n Vector

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SUMMARY

The discussion focuses on calculating torque using the equation t = n dot (r X F), where 'n' is the unit vector. To find the unit vector 'n' for a specific line, such as x/2 = y/1 = z/-2, participants suggest identifying two points on the line and using the position vector derived from these points. If the resulting vector is not of unit length, it must be normalized by multiplying it by a constant to achieve a length of one.

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  • Understanding of torque and its calculation
  • Familiarity with vector operations, including dot product and cross product
  • Knowledge of unit vectors and normalization techniques
  • Basic skills in solving parametric equations of lines in three-dimensional space
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  • Learn how to derive unit vectors from parametric equations
  • Study normalization of vectors in three-dimensional space
  • Explore the application of torque in physics problems
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Students preparing for physics exams, educators teaching vector mechanics, and anyone interested in mastering torque calculations in three-dimensional space.

Vertol
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I know how to find a torque at anyone point, and about the x,y, and z axis.

General equation is t = n dot (r X F)

where t is the torque, n is unit vector

I know that to find torque about any axis, suppose the y-axis then n=(0,1,0) However, I don't know how to find n of any line.
I am working on a practice problem for a test where the line is x/2 = y/1 = z/-2

Any help would be appreciated.
 
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find 2 points on the line, use the position vector of point2 - point1.

If this vector has length 1 you're done. If not, multiply the vector by
some constant to make the length equal to 1.
 

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