- #1
jaejoon89
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"The vertices of a regular tetrahedron are OABC. Prove that vector OA + OB + OC is perpendicular to plane ABC."
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No idea how to do this. Please help.
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No idea how to do this. Please help.
A vector proof is a mathematical method used to demonstrate the validity of a statement or theorem involving vectors. It involves using algebraic and geometric properties of vectors to show that the given statement is true.
To write a vector proof, you need to clearly state the given statement or theorem, and then break it down into smaller parts. You can then use algebraic and geometric properties of vectors to manipulate the equations and show that each part is equal, thus proving the statement to be true.
Some common properties used in vector proofs include the commutative, associative, and distributive properties of vector addition and scalar multiplication, as well as the properties of vector dot and cross products.
Yes, vector proofs can be used to prove non-geometric statements as long as the statements involve vectors and their properties. For example, vector proofs can be used to prove equations involving forces in physics or displacement in engineering.
One common mistake to avoid when writing a vector proof is to assume that the given statement is true without properly proving it. It is important to break down the statement into smaller parts and show the logical steps used to prove each part. Additionally, it is important to be familiar with the properties of vectors and use them correctly in the proof.