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Is there a way to mirror the existing position of the 3D cursor over to the (camera right) left side of this vehicle so that I can place the pivot point exactly where it is in relation to the right car's pivot?

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In my example I assume you want to mirror the Y location of the 3D cursor.

If the Y center of the car is at zero, simply change the sign of the Y coordinate of the 3D cursor (let's call it B, make it -B).

If its not zero it will have a value (let's call it A), you can copy it hovering over its transform value in the "N" properties panel and pressing Ctrl C.

Then go to View > 3D cursor, click on the Y value of the location of 3D cursor, change its sign and type + 2*(Ctrl V), because the formula is 2A - B.

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