Torque Calc: Find Torque from Force F, Vector r

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The discussion focuses on calculating the torque acting on a pebble due to a force vector F and a position vector r. The torque is determined using the cross product of the vectors, specifically τ = r x F. Participants clarify that the force vector should be positioned with its tail at the origin for accurate calculation. Additionally, they suggest using the determinant method for computing the cross product. The conversation concludes with a participant confirming they have resolved their initial confusion.
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Force F = (4.59 N)i - (6.29 N)k acts on a pebble with position vector r = (3.46 m)j - (4.51 m)k, relative to the origin. What is the resulting torque acting on the pebble about (a) the origin and (b) a point with coordinates (3.16 m, 0, -4.97 m)?*The force F is a vector, as is r, I just don't know how to get the vector symbol above it. i, j, k are "i hat, j hat, k hat, I don't know how to get the symbol above those either. Sorry, only my second post.

Attempt at a solution:

I have no idea where to begin. I think the answer will be the cross product of r x F, but our book doesn't give a good example of cross products. Wouldn't you shift the force vector so that the tail is at the origin O?
 
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\mathbf{\tau} = \mathbf{r} \times \mathbf{F}[/tex]<br /> You can compute the cross product in terms of components. <br /> <br /> For two vectors \mathbf{a} = a_x \hat{\imath} + a_y \hat{\jmath} and \mathbf{b} = b_x \hat{\imath} + b_y \hat{\jmath}, \mathbf{a} \times \mathbf{b} = (a_xb_y-a_yb_x) \hat{k}.<br /> <br /> You can get this by FOIL-ing the terms or writing the cross product as a 3 x 3 matrix and taking the determinant:<br /> &lt;br /&gt; \mathbf{a} \times \mathbf{b} = \begin{vmatrix}&lt;br /&gt; \hat{\imath} &amp;amp; \hat{\jmath} &amp;amp; \hat{k} \\&lt;br /&gt; a_x &amp;amp; a_y &amp;amp; 0 \\&lt;br /&gt; b_x &amp;amp; b_y &amp;amp; 0&lt;br /&gt; \end{vmatrix}&lt;br /&gt;<br /> <br /> For part b, find the new displacement vector from the point to the point defined by r.
 


Thanks! I got it.
 
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