Vector Multiplication: a-b X a+b = 2(aXb)

In summary, the conversation is discussing the equation (a-b)X(a+b)=2(aXb), where a and b are vectors. The speaker suggests starting with the definition of cross multiplication and expanding the equation using the given vectors. Another speaker suggests using the distributive property of the cross product to simplify the equation.
  • #1
physicsss
319
0
(a-b)X(a+b)=2(aXb), where a and b are vectors.

Thank you.
 
Physics news on Phys.org
  • #2
What have you tried so far?

I would start with the definition of cross multiplication.
 
  • #3
I tried to set a=<x,y,z> and b=<x1,y1,z1> and expand everything...and the left side became a big mess.
 
  • #4
Why don't u multiply exactly what u were given...?I mean there are exactly 4 cross products u'd be getting,when doing it.2 of them are 0...

Daniel.
 
  • #5
The cross product is distributive. Use that and some of its other properties to get the answer. No need to fiddle with components.
 

Related to Vector Multiplication: a-b X a+b = 2(aXb)

1. What is vector multiplication?

Vector multiplication is a mathematical operation performed on two vectors to produce a third vector. It is used to find the direction and magnitude of the resulting vector when two vectors are combined.

2. How is vector multiplication different from scalar multiplication?

Vector multiplication involves two vectors, while scalar multiplication involves a vector and a scalar (a single number). Vector multiplication results in a vector, while scalar multiplication results in a number.

3. What is the formula for vector multiplication?

The formula for vector multiplication is a-b X a+b = 2(aXb). This formula is used specifically for multiplying two vectors that are parallel and perpendicular to each other.

4. Why is the resulting vector twice the magnitude of the original vectors?

The resulting vector is twice the magnitude of the original vectors because it is the sum of two multiplied vectors. In other words, the resulting vector represents the combined effect of both original vectors.

5. What is the significance of vector multiplication in science?

Vector multiplication is important in science because it allows us to calculate the effect of multiple forces acting on an object. It is used in physics, engineering, and other fields to model and understand the behavior of various systems.

Similar threads

B Some questions while I self-learn Applied Calculus
    • Calculus
2
Replies
46
Views
2K
I The Vector Laplacian: Understanding the Third Term
    • Calculus
Replies
6
Views
723
B What is the Significance of the Laplace Operator in Vector Calculus?
    • Calculus
Replies
6
Views
961
I Definition of Limit for vector fields
    • Calculus
Replies
6
Views
1K
I Curvature of 3D Graph on Point w/ Directional Vector
    • Calculus
Replies
3
Views
1K
I Why prove Taylor's theorem with p(x)=q(x)−((b−a)^n/(b−x)^n)q(a)?
    • Calculus
Replies
9
Views
1K
I Lipschitz continuity of vector-valued function
    • Calculus
Replies
3
Views
1K
I ##L^2## square integrable function Hilbert space
    • Calculus
Replies
11
Views
418
MHB Are $\vec{r}$ and $\frac{d^2\vec{r}}{dt^2}$ Parallel When m+n=1?
    • Calculus
Replies
6
Views
1K
MHB Proving Equation (1): Let r(t) be a Vector in $\mathbb{R^3}$
    • Calculus
Replies
2
Views
783

Hot Threads

Recent Insights

Back
Top