1. If a and b are collinear, b and c are collinear? 2. If the module of vector a+b is equal to the module of vector a-b, is a multiplied by b=0? 1. If a and b are collinear, then a and c are collinear? 2. If the module of vector a+b is equal to the module of vector a-b, is a multiplied by b=0?

1. If a and b are collinear, b and c are collinear? 2. If the module of vector a+b is equal to the module of vector a-b, is a multiplied by b=0? 1. If a and b are collinear, then a and c are collinear? 2. If the module of vector a+b is equal to the module of vector a-b, is a multiplied by b=0?

The first one is not necessarily because if b is a zero vector then it is collinear with any vector. The second is correct
The module of vector a+b and the module of vector a-b can be regarded as two diagonal lines of a rectangle, and the adjacent sides of the rectangle are perpendicular to each other, of course ab=0

How to prove that A, B and C are collinear (with vector)

Prove (vector AB)=k (vector BC), if the coordinates are known, vector AB, BC can be expressed in coordinates
K is a constant

I want to ask a vector question, vector (a, b) and vector (a-2, b-2), a # b, ask: are they collinear vectors? I don't think so, because the slope of the line where the two vectors are located is different, but can you look at it this way: shift (a, b) two unit lengths to the left, and then shift two unit lengths down, is n' t that (a-2, b-2)? Who can tell me in detail Better have an illustration. I want to ask a vector question, vector (a, b) and vector (a-2, b-2), a # b, ask: are they collinear vectors? I don't think so, because the slope of the line where the two vectors are located is different, but can you look at it this way: shift (a, b) two unit lengths to the left, and then shift two unit lengths down, is n' t that (a-2, b-2)? Who can tell me in detail Preferably with illustrations

Translate (a, b) to the left by two unit lengths, and then to the bottom by two (a-2,
B-2)? No! No! After translation, the vector ends at (a-2, b-2) and the start at (-2,-2)
Vector or (a, b).

If the vector a, b satisfies |a+b|=|b|, then what is a+b=?

A/2, square on both sides

If vector a is an arbitrary vector vector b collinear with vector a then vector b=

B=ka, k is any real number not equal to zero.
Upstairs, two places.

B=ka, k is any real number not equal to zero.
Upstairs, two digits.

The projection of a vector on b vector The formula should be |a|.|b|cosθ How does it translate into (a.b)/|b|

A projection in direction b:|a|cos
Not:|a b|cos ---------This is the number product of a and b
|A|cos=|a b|cos/|b|=a·b/|b|

A Projection in b direction:|a|cos
Not:|a b|cos ---------This is the product of a and b
|A|cos=|a b|cos/|b|=a·b/|b|