Right Hand Rule (👉)for Cross Product of Vectors ❎
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- Опубликовано: 15 окт 2024
- Vector product or the cross product of two vectors “a” and “b” that are φ degrees apart is written as aXb and the result of this operation is a third vector c that equals “a b Sine φ”.
The resultant vector c is a vector that is perpendicular to both the vectors a and b. What is important to remember is that φ is the smaller of the 2 possible angles… that is φ or 360 - φ (because Sin φ is not equal to Sin (360 - φ). Recall, in dot product you could take any of the angles.
You might think that vector perpendicular to a and b could be two direction. To determine the correct direction, this is what you do: put your right hand along vector “a” which is the first vector appearing in aXb, that is the base of the hand aligns with vector a and the palm of your hand faces vector b. Then if you sweep your hand from vector a towards vector b, the direction of the thumb is the correct direction of the resultant vector c.
Cross Product of two Vectors: • Cross Product of Two V...
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thankyou so much, ive been looking for an explanation and couldnt understand any video no matter how much i tried, you explain so well thankyou!!!!!
Delighted to know that 😀 . Where are you from Alin?
I think we should curve our fingers instead of sweeping the hand. Am i right?
You could do either as long as you are interpret the meaning of either. The hand or fingers are just an aid
@@TheScienceCube hmm, make sense Ok!
Good explanation ❤
Hello Vaishnavi! do join our Telegram Channel 🔗t.me/TheScienceCube_Community where the exploration never stops! I cover,
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But between a and b, how do we determine a or b comes first which affects the direction of c?
Good question. Cross product is always specified. That is which vector comes first is defined. As an example torque is the cross product of r and F and is written as t = rxF and not as Fxr. So you would not have to decide which one should come first
Nice explain
Hi Narangi! Please also join my Telegram t.me/TheScienceCube_Community for PDF lesson summaries and other physics solutions. You can always leave if you wish to, but trust me, you won't want to miss this! 😉
Why sin?
The sine function has a critical property that it is zero when the angle is 0 degrees or 180 degrees, which aligns with the physical interpretation of the cross product. When two vectors are parallel or anti-parallel, the 'area' spanned by them is zero, and hence, their cross product should be a zero vector, which is what happens due to the sin(0 degrees) = 0 and sin(180 degrees) = 0.
@@TheScienceCube I meant why cross product have sine and dot have cosine
@@krishna290gamer2 Yes I understood your question. See, the cross product is designed to find a vector that is perpendicular to both vectors A and B. The magnitude of this vector depends not only on the lengths of vectors A and B but also on how they are oriented with respect to each other. The sine of the angle between them gives a measure of how spread out vectors A and B are.
Geometrically, the magnitude of the cross product corresponds to the area of the parallelogram spanned by vectors A and B. The formula for this area is base times height, where the base is the length of vector A, and the height is the length of vector B times the sine of the angle between them. This is because the sine of the angle gives the ratio of the opposite side to the hypotenuse in a right-angled triangle, translating here to how much of vector B is effective in spanning the area perpendicular to vector A. Now you read what i wrote earlier and it will make more sense.
@@TheScienceCube thanks sir
@krishna290gamer2 Krishna I am sure this is still not very clear to you. I'd encourage you to read more about this on some authentic websites.
Why we put sin in this formula?
Well there are several reasons. In summary - the use of sine in the cross product conveys the geometric relationship between two vectors in terms of their magnitude, orientation, and the area of the parallelogram they enclose. In a way it ensures the resultant vector correctly represents both the magnitude and the direction of their mutual perpendicularity.
thank U sir
Hi Mohammad! Please also join my Telegram t.me/TheScienceCube_Community for PDF lesson summaries and other physics solutions. You can always leave if you wish to, but trust me, you won't want to miss this! 😉