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I actually dont understand that when do we use cross product and when to use dot product ……it is very difficult to remember that a torque is cross product and work done is dot product. please tell me the reasons behind these so that i can understand the concept not just blindly memorize?

Qmechanic
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Physics student
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  • Torque is a vector (an axial vector if we're pedantic), while work is a scalar. Do you wish to ask why that is so, or do you understand it? Because that's enough information to work out which product to use. – J.G. Aug 17 '23 at 10:03
  • Yeah please explain more to me…. – Physics student Aug 17 '23 at 10:05
  • A torque cannot be completely defined without giving it a sense of rotation i.e. clockwise vs anticlockwise. So torque couldn't be defined using a dot product since that gives a scalar output. – AVS Aug 17 '23 at 10:47
  • Why is work a scalar: https://physics.stackexchange.com/questions/418187/why-is-work-scalar-and-the-dot-product-of-force-and-displacement?rq=1 – AVS Aug 17 '23 at 10:49
  • Related https://physics.stackexchange.com/a/516069/392 – John Alexiou Aug 17 '23 at 12:17
  • Does https://physics.stackexchange.com/a/518467/392 answer your question, as far as the cross products at least? – John Alexiou Aug 17 '23 at 12:18
  • The simplest intuition is given by https://physics.stackexchange.com/a/37884/392 – John Alexiou Aug 17 '23 at 12:38

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The cross product's output is a vector and it tells you how much of the two vectors are at right angles to each other. The cross product of parallel vectors is zero. The cross product of two perpendicular vectors is another vector in the direction perpendicular to both of them with the magnitude of both vectors multiplied.

The dot product's output is a number (scalar) and it tells you how much the two vectors are in parallel to each other. The dot product of two parallel vectors is the product of their lengths. The dot product of two vectors at right angles to each other is zero.

Suzu Hirose
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