Why is it necessary to add the unit vectors of two straight lines to find the direction vector of the bisector of the angles of two straight lines Is it possible to add the direction vectors of the two lines as the direction vectors of the bisector

Why is it necessary to add the unit vectors of two straight lines to find the direction vector of the bisector of the angles of two straight lines Is it possible to add the direction vectors of the two lines as the direction vectors of the bisector

(1) The direction vector of the bisector cannot be the sum of the direction vectors of two straight lines
(2) You can add the unit direction vectors of the two lines as the direction vectors of the bisector
Or the direction of two lines can be vectorized into the form of modulus equality
The reason is the parallelogram rule of addition,
If the diagonal is an angular bisector, it must be a diamond, so the modules of two vectors must be equal

Coordinate operation of plane vector: two vectors are collinear, how to judge whether the direction is the same or reverse?

Let a = (x1, Y1) and B = (X2, Y2)
Because vector a and vector B are collinear, so x1y2-x2y1 = 0, that is, X1 / x2 = Y1 / Y2
If X1 / x2 = Y1 / Y2 > 0, then vector a and vector B are collinear in the same direction;
If x 1 / x 2 = Y 1 / y 2 ＜ 0, then vector a and vector B are inversely collinear
Or, vector a = λ vector B
(x1,y1)=λ(x2,y2).
=(λx2,λy2).
If x 1 = λ x 2, x 1 / x 2 = Y 1 / y 2 = λ, λ > 0, the two vectors are collinear in the same direction; if λ < 0, the two vectors are collinear in the opposite direction

What is the geometric and physical meaning of the addition of two vectors?
1. What is the geometric and physical meaning of the addition of two vectors?
2. What is the geometric meaning of the size of the vector product of a vector?

1
The addition of vectors is geometrically represented as a closed graph. The sum of several vectors is the directed line segment from the beginning to the end
Physical meaning: the effect of combined vector = the combination of several sub vector effects (force, displacement, velocity, acceleration, etc.)
2. The product of vectors
(1) Dot product: a * b = abcos α (α is the angle between a vector and B vector)
The dot product represents the projection length of a (or b) vector on B (or a) vector, which is scalar
(2) Cross product: AXB = absin α (α is the angle between a vector and B vector)
The cross product represents the area of a parallelogram adjacent to vector a and B. It is a vector and its direction is right-handed helix. The four fingers of the right hand bend from a to B, and the thumb refers to the cross product AXB direction. AXB and BXA are opposite

No matter how big the angle AB + AC is, AB + AC = BC

OK, let's talk about the addition and subtraction of vectors: as you said, generally two upper case letters are used to represent vectors, or a lower case letter is used to represent vectors. If a represents vector AB and B represents vector AC, then a + B = AB + AC represents a diagonal line of a parallelogram with AB and AC as adjacent sides, point a is the common starting point, B-A = ac-ab = BC