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Course: Physics library>Unit 13

Lesson 1: Magnets and Magnetic Force

Cross product 1

Introduction to the cross product. Created by Sal Khan.

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• at when sal said orthagonal what does that mean?
• Perpendicular.
• What is the difference between fleming's right hand rule and fleming's left hand rule? Which one is used to find the direction of force? Sal uses his right hand but in my physics book it says to use my left hand.
• I'm not sure what your particular book says, but the right hand rule is always applicable for cross products. There are two possible things I can think of to explain. The less probably one is that your physics book gives instructions on using the left hand that are equivalent to using the right hand. For example, if you used your left index finger for Sal's a-vector, and your left thumb for Sal's b-vector, your left middle finger would point in the direction of n-hat. The right hand rule is fairly standard, though, so I would guess this is not the case.

The other, more probably explanation is that your book is talking about the right hand rule with regards to electrons in magnetic fields. In electricity and magnetism, the convention is that field lines point in the direction that a POSITIVE charge would move. An electron, being negatively charged, would move in the opposite direction. The force from a magnetic field is F=q(vxB), where v is the velocity of the particle and B is the magnetic field vector. So, you'd use the right hand rule to find the direction a positive charge would move. Alternatively, you could use the left hand rule to find the direction that an electron would move.
• Why do we know that the vector has to be perpendicular to the other two?
• Hi Chris,
I'm not too keen on physics but, things like cross product are abstract representations of physical models of things. So at some point, "that's how you define it" I think is really as basic as you can get. We don't fundamentally know why the basic laws of arithmetic work but we defined this system to describe it. I think its similar when there was a need to define something called a cross product.
• Actually, I can't understand all of the explaination. However, I have a question. why in cross product we use sin? can you give the explaination. and also in dot product why we use cos? thank you.
• what is basic definition of a unit vector
• a unit vector is a vector whose magnitude is 1 and is along a particular direction
• If we switch vector a and vector b, does that mean their product will be coming out of the page? Does that mean a times b is equal to the opposite of b times a?
• This is correct. The direction can be visualized by the Right Hand Rule. Taking vector A X B will give you the opposite direction of B X A.

In addition, further proof that the magnitude will be the same is found in the formula: |A||B|sin θ = |A X B|.
Since scalar multiplication is not dependent on the order in which it is preformed, the magnitude will be the same in both cases.
• around , you use the right hand rule. is it easier to use the right hand screw rule? (same as the one used to find the direction of magnetic field in a current carrying conductor)
• There are various conventions that can be used for a right-hand rule. Here is a good video that explains 4 different ways. This guy will make you laugh because he is a bit strange. As for method, I prefer thumb pointing in direction of vector A, index finger pointing in direction of vector B. Your middle finger then points in the direction of the n unit vector. http://www.youtube.com/watch?feature=fvwp&v=LK7hv4LX3ys&NR=1
• Okay, so I understand the cross product, how it works and its formula but what is it actually, I mean what is a cross product?