Can the Resultant of Cross Products of Vectors with Zero Resultant also be Zero?

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In summary, the speaker has made a conclusion about a vector-related problem and wants to prove it on their own. They believe that if a number of vectors with a resultant of zero are crossed with a non-zero vector, the resultant of the cross results will also be zero. They clarify that this statement is essentially the distributive law for cross product. They thank another person for their assistance and plan to share their proof once it is refined.
  • #1
STAii
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Greetings !
I have made a conclusion while investigating some vector-related problem.
I am currently trying to proove it (i am sure that if it is true, lot of you would be able to proove it, but i prefer to try that myself for the moment).
What i need is only to know whether or not my conclusion is right.
Here it is :
"If you have a number of vectors (say n) that have a resultant of Zero, and you cross each one of them with a non-zero vector, then find the resultant of the cross results, then it will be zero too"
If this is not really clear, i will try to make it clearer.
Thanks.
 
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  • #2
In other words, the distributive law holds for cross product:

u x (v+ w)= u x v+ u x w. In the special case that v+ w= 0,

u x v+ u x w= u x 0= 0.
 
  • #3
Thanks HallsofIvy.
I think i figured out how to proove it even without using distributive law (actually, i didn't know that it holds for cross product).
I will make sure i am not wrong, make everything 'mathematically beautiful' then put it here.
 

1. What is a vector?

A vector is a mathematical quantity that has both magnitude and direction. It is commonly represented by an arrow pointing in the direction of the vector, with its length representing the magnitude.

2. How do you confirm if a vector is true?

To confirm if a vector is true, you need to check if it satisfies the properties of a vector. These include having both magnitude and direction, being able to be scaled by a scalar, and being able to be added to other vectors.

3. What is the difference between a vector and a scalar?

A vector has both magnitude and direction, while a scalar only has magnitude. This means that a vector can be represented by an arrow, while a scalar is represented by a single number.

4. How are vectors used in science?

Vectors are used in science to represent physical quantities, such as velocity, acceleration, and force. They are particularly useful in physics and engineering to describe the direction and magnitude of these quantities.

5. Can two vectors with different directions be equal?

No, two vectors with different directions cannot be equal. Vectors are only considered equal if they have the same magnitude and direction. If the directions are different, then the vectors are not equal, even if their magnitudes are the same.

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