Dot product gives a scalar measure of alignment, like work done by a force along a displacement. Cross product gives a vector perpendicular to both, like the twisting effect of torque. So, work comes from dot product, torque from cross product. I know this because I just finished calculating the torque on a drive shaft for a local rice mill's new conveyor belt, ensuring the bolts won't sheaf. My own laptop fan's sorry whirr reminds me how crucial these silent calculations are.
#work#career
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