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I have two doubts regarding this concept

1- why do we do the cross product? and what does the resultant vector actually represent? and does the resultant vector actually mathematically be perpendicular to these two input vectors or did we just use the third dimension in order to represent the area of the parallelogram for our convenience?

2- what is the cross product of two force vectors called? and If there really is such a thing in this world then where do we use it? and Does the resultant vector point towards the perpendicular direction of these two force vectors?

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  • $\begingroup$ At least the first question has been asked and answered many times already, see for example math.stackexchange.com/questions/1395970/… and the linked questions there. $\endgroup$
    – Hans Lundmark
    Commented Apr 17, 2020 at 10:35
  • $\begingroup$ To answer the last part of Q2, the cross product should be perpendicular to both force vectors. Unless the two forces are going in the same direction (or have an angle of 180 degrees between them, in which case the cross product is zero). $\endgroup$
    – 1123581321
    Commented Apr 19, 2020 at 9:42

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The cross product or vector product is defined as it is because it is a useful concept in physics, and helps us write down physical laws and equations of motion in a concise way - especially laws involving angular momentum, moments of forces, torques and the interaction of magnetic fields and electric charges (as in the Lorentz force equation).

Mathematically, the cross product of two vectors is a less "natural" concept than the dot or scalar product, and it does not generalise to higher dimensions as simply as the scalar product does.

I cannot think of a physical example where the cross product of two force vectors is physically meaningful, and I don't think it has a specific name.

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  • $\begingroup$ thank you ...making your time to answer this. by chance would you know why does the vectors cross product end up resulting a vector which is perpendicular to the input vectors. the concept of i * j = k is it just created for readability or we really do get a perpenducular vector to the 2 dimensional plane. $\endgroup$
    – kevin godfrey
    Commented Apr 17, 2020 at 11:45

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