It's not true.Bipolarity said:Homework Statement
If [itex] (a \times b) \times (c \times d) = 0 [/itex], show that a,b,c,d are coplanar.
Homework Equations
The Attempt at a Solution
I have done the converse of this problem, but am having trouble on how to do this. Can we perhaps use Lagrange's identity. How can I start?
BiP
SammyS said:It's not true.
If [itex](a \times b)=0\,,[/itex] the c & d can be anything.
A vector is a mathematical object that has both magnitude (or size) and direction. It can be represented by an arrow, with the length of the arrow representing the magnitude and the direction it points in representing the direction.
A vector proof is a mathematical argument or demonstration that uses the properties and operations of vectors to show that a certain statement or equation is true.
Vector proofs are important because they help us understand and apply the principles of vectors in various mathematical and scientific fields, such as physics and engineering. They also help us to develop problem-solving skills and logical thinking.
To write a vector proof, you first need to clearly state the statement or equation you want to prove. Then, you can use the properties and operations of vectors, such as addition, subtraction, and scalar multiplication, to manipulate the given information and arrive at the desired conclusion.
Common mistakes to avoid in a vector proof include incorrect use of vector operations, not clearly stating the given information and desired conclusion, and not providing enough justification or explanation for each step of the proof. It is also important to check for errors and ensure that the proof is logically sound and follows the rules of vector algebra.