Problem with vector operator

In summary, the coordinate system expressed in terms of x, y, z is more common, but the mathematical identity holds for any two vectors.
  • #1
moatasim23
78
0
Why do we use the coordinates of r in terms of x,y,z?Why don't we express coordinates of A in x,y,z?
 

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  • #2
A is expressed in terms of x y and z.
 
  • #3
It's a matter of notation: we're just giving names to the three components of both vectors.
You can replace them by ##r_1, r_2, r_3##, if that makes you feel any better. In general, if v is a vector, it is customary to denote its components by v1, v2, v3. However, if r is the position vector, then (x, y, z) is also quite common.

Also note that though the fact that one is named r hints that it comes from a physical application in which a position vector is involved, the mathematical identity actually holds for any two vectors u, v.
 
  • #4
No its not..here at least
 
  • #5
CompuChip said:
It's a matter of notation: we're just giving names to the three components of both vectors.
You can replace them by ##r_1, r_2, r_3##, if that makes you feel any better. In general, if v is a vector, it is customary to denote its components by v1, v2, v3. However, if r is the position vector, then (x, y, z) is also quite common.

Also note that though the fact that one is named r hints that it comes from a physical application in which a position vector is involved, the mathematical identity actually holds for any two vectors u, v.

If we use r1,r2,r3 then how would the vector operator operator operate on it?Like it didnt in A when we used A1,A2,A3.
 
  • #6
What are you talking about?
 
  • #7
moatasim23 said:
No its not..here at least
I'm sorry - the example in your attachment very clearly states that

A=A1i+A2j+A3k

That means that
- the x component of A is A1,
- the y component of A is A2,
- the z component of A is A3.

Therefore: A is resolved in terms of x, y, and z.

What did you think it meant?
 
  • #8
I don't understand your question, I think.

If ##\mathbf v = v_1 \mathbf i + v_2 \mathbf j + v_3 \mathbf k## and ##\mathbf u = u_1 \mathbf i + u_2 \mathbf j + u_3 \mathbf k## then
$$\mathbf u \times \mathbf v = (u_2 v_3 - u_3 v_2) \mathbf i + (u_3 v_1 - u_1 v_3) \mathbf j + (u_1 v_3 - u_3 v_1) \mathbf k$$

That's just how the cross product works. It doesn't matter how you call the components. You could replace ##u_1##, ##u_2## and ##u_3## by ##x##, ##y## and ##z## or clubs, spades, hearts or bunny, cow, eagle and the definition would still be the same.

Is it the notation of a vector like##\mathbf v = v_1 \mathbf i + v_2 \mathbf j + v_3 \mathbf k## instead of ##\mathbf v = (v_1, v_2, v_3)## that confuses you?
 

1. What is a vector operator?

A vector operator is a mathematical operation that acts on a vector quantity, resulting in another vector quantity. It is commonly used in fields such as physics and engineering to represent physical quantities that have both magnitude and direction.

2. What are some common problems with vector operators?

Some common problems with vector operators include difficulty in visualizing vector operations, confusion between vector and scalar quantities, and the potential for mathematical errors due to the complexity of vector algebra.

3. How are vector operators different from scalar operators?

Vector operators act on vector quantities, which have both magnitude and direction, while scalar operators act on scalar quantities, which only have magnitude. Additionally, vector operators follow different mathematical rules and require more complex calculations compared to scalar operators.

4. What are some practical applications of vector operators?

Vector operators have many practical applications in various fields such as physics, engineering, and computer graphics. They are used to represent physical quantities such as force, velocity, and acceleration, and to solve problems involving vector quantities.

5. How can I improve my understanding of vector operators?

To improve your understanding of vector operators, it is important to first have a strong foundation in vector algebra and trigonometry. You can also practice visualizing vector operations and solving problems involving vector quantities. Additionally, seeking help from a tutor or joining a study group can be beneficial in improving your understanding of vector operators.

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