How to find the area of triangle with known vector? Given the vector OA = (2,3), OB = (3, - 3), then the area of triangle OAB is? I saw a formula from others Cos θ = vector AB * vector ob / | vector ab | * | vector ob| I don't understand what it means. We didn't learn the relationship between vector and trigonometric ratio. I don't understand this formula. I want to learn some knowledge How to solve vector operation

How to find the area of triangle with known vector? Given the vector OA = (2,3), OB = (3, - 3), then the area of triangle OAB is? I saw a formula from others Cos θ = vector AB * vector ob / | vector ab | * | vector ob| I don't understand what it means. We didn't learn the relationship between vector and trigonometric ratio. I don't understand this formula. I want to learn some knowledge How to solve vector operation

Two vector dot multiplication (not multiplication), their relationship is: vector AB * vector ob = | vector ab | * | vector ob | * cos θ, θ refers to ∠ AOB, this is vector operation, since it is a vector problem, there should be learning vector operation, if not, it doesn't matter, vector operation is a sophomore in high school, you will learn sooner or later, such as

The coordinate representation of space vector operation is known as a (1,0,0), B (0,0,1), C (0,0,2), and the point D coordinate satisfying the following requirements is obtained
DB ⊥ AC, DC ⊥ AB and ad = BC

The basic idea is as follows:
Let D (x, y, z);
Then the vector BD (x, y, Z-1);
Vector Ca (1,0, - 2);
Vector CD (x, y, Z-2);
Vector BA (1,0, - 1);
Vector ad (x-1, y, z);
Vector BC (0,0,1);
Then the vector product (BD, CA) = 0
Vector product (CD, BA) = 0
(x-1)*(x-1)+y*y+z*z=1;
Three equations, find out x, y, Z is OK
However, I don't know if there is a problem with LZ's topic, or if there is a mistake in my process, I can't solve it. Please check with LZ

Parallel coordinate problem of space vector
If a is parallel to B, what is the relationship between a (x, y, z) and B (a, B, c)?
If two-dimensional is not parallel, then x1y2 = x2y1, I want to ask three-dimensional

For space vector, each vector has three coordinate values. As a simple judgment of parallel (collinear) relationship, it only needs their coordinates to be proportional. If it has to be written in the form of product, it must be written as XB Ya = 0, XC Za = 0, YC ZB = 0, and it must be true at the same time

High school space vector
Vector N1 = (1,1,0)
Vector N2 = (1,2,1)
The teacher said cosa = internal product divided by the product of modules, what is internal product, how to calculate, and what is the final result?

The inner product is the quantity product
n1.n2=1*1+1*2+0*1=3
|n1|=√(1+1+0)=√2
|n2|=√(1+4+1)=√6
∴ cosa=3/(√2*√6)=1/2
The angle between the vectors is 60 degrees