Vector Triple Product: Are a & c Parallel or Collinear?

In summary, the conversation discusses the use of a specific statement in books regarding vectors and their cross product. The statement states that (axb)xc is not equal to ax(bxc), but if they are equal, then bx(axc) must equal 0. This leads to the conclusion that either b is parallel to (axc) or a and c are collinear. The question is raised whether a and c can be considered parallel instead of collinear, as stated in most books. The speaker suggests that in general, a and c do not have to lie in the same line to be considered collinear.
  • #1
debjit625
40
0
Hi all got a confusion
In many books I saw , authors used a specific statement here is it

a,b,c are vectors and axb is (" a cross b")
In general
(axb)xc ≠ ax(bxc)
but if
(axb)xc = ax(bxc)
solving it we get
bx(axc)=0
then it implies
either b is parallel to (axc)
or a and c are collinear.

Now my question is can I say a and c are parallel rather co linear ,my confusion arise as all books I referred they all say its co linear.

Now I think in general a and c doesn't have to lie in a same line to get the specific definition of co linearity ,
but I am not sure.

Thanks
 
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  • #2
In 3D we represent a vector with three numbers (x,y,z)
All vectors 'start' in (0,0,0), so if they are parallel they are also colinear (one is a multiple of the other).
 

FAQ: Vector Triple Product: Are a & c Parallel or Collinear?

1. What is a vector triple product?

A vector triple product is a mathematical operation that involves three vectors. It results in a vector that is perpendicular to both of the initial vectors.

2. How is the vector triple product calculated?

The vector triple product is calculated using the cross product of two vectors, followed by the dot product of the resulting vector with a third vector.

3. What is the significance of the vector triple product?

The vector triple product is often used in physics and engineering to calculate moments and torques, as well as in vector calculus and linear algebra to demonstrate mathematical concepts.

4. Are the vectors a and c parallel or collinear in a vector triple product?

In a vector triple product, the vectors a and c are not necessarily parallel or collinear. It depends on the values of all three vectors and their orientations.

5. What are some real-world applications of the vector triple product?

The vector triple product has various applications in fields such as mechanics, electromagnetism, and quantum mechanics. For example, it is used in calculating the magnetic moment of a current loop and the angular momentum of a spinning object.

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