Proof of $(A+B) \times (A-B) = -2(A \times B)$, where 'A' and 'B' are vectors
2026-03-28 22:27:07.1774736827
Proof of $(A+B) \times (A-B) = -2(A X B)$
8.5k Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in VECTORS
- Proof that $\left(\vec a \times \vec b \right) \times \vec a = 0$ using index notation.
- Constrain coordinates of a point into a circle
- Why is the derivative of a vector in polar form the cross product?
- Why does AB+BC=AC when adding vectors?
- Prove if the following vectors are orthonormal set
- Stokes theorem integral, normal vector confusion
- Finding a unit vector that gives the maximum directional derivative of a vector field
- Given two non-diagonal points of a square, find the other 2 in closed form
- $dr$ in polar co-ordinates
- How to find reflection of $(a,b)$ along $y=x, y = -x$
Related Questions in CROSS-PRODUCT
- Proof that $\left(\vec a \times \vec b \right) \times \vec a = 0$ using index notation.
- Why is the derivative of a vector in polar form the cross product?
- Calculus III Vector distance problem.
- linear algebra - Parallel vectors
- Geometry of the plane in 3D and cross product
- derivative of cross product of vectors with respect to vector
- Finding perpendicular and parallel vectors
- Why is the unit vector negative when solving $\sin(a-b) = \sin(a)\cos(b) - \cos(a)\sin(b)$?
- A question about cross product
- Linear Algebra: Cross Product w/ Matrices
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
Using the distributive law, $$(A+B)\times(A-B)=A\times A-A\times B+B\times A-B\times B$$ $$A\times A=B\times B=0$$ $$(A+B)\times(A-B)=0-A\times B+B\times A-0$$ $$B\times A=-A\times B$$ $$(A+B)\times(A-B)=-A\times B-A\times B=-2(A\times B)$$