△The lengths of the opposite sides of the three internal angles A, B and C of ABC are a, b and c respectively. Let the vector P=(a+c, b), Q=(b−a, c−a), if P∥ Q, the size of angle C is ______.

Because

P∥

Q, get
A+c
B−a=b
C−a: b2-ab=c2-a2
I.e. a2+b2-c2=ab
By cosine theorem cosC=a2+b2−c2
2Ab=1
2
So C=π
3
Therefore, the answer is:π
3

Vector a parallel b, b parallel c, prove a is not parallel c

B can be a zero vector, which is parallel to any vector, so that a and c are not parallel.

If vector a runs parallel to vector c (vector a·vector b)·vector c=vector a·(vector b·vector c) If it doesn't, under what circumstances?

Yes, very simple.
If c is a zero vector, it obviously holds.
If c is not a zero vector, because a//c
Therefore, a=kc
So (a·b) c=(kc·b) c=k (c·b) c
A (b·c)=(b·c) a =(b·c)(kc)=k (c·b) c
Apparently equal
Note that the point product is a real number

Yes, very simple.
If c is a zero vector, it obviously holds.
If c is not a zero vector, because a//c
Therefore, a=kc
So (a·b) c=(kc·b) c=k (c·b) c
A (b·c)=(b·c) a =(b·c)(kc)=k (c·b) c
Apparently equal
Note that the product is a real number.

Given that the vectors a, b are not collinear, if there is a vector c so that a is parallel to c, b is parallel to c, then what is c, who knows Given that the vectors a, b are not collinear, if the vector c exists so that a is parallel to c, b is parallel to c, then what is c, who knows

0 Vector

Vector b is collinear with vector a, b=ka, why a is not equal to 0

Parsing:
Your question is wrong.
Should be vector b and vector a collinear, b=ka, why k is not equal to 0
Because k =0, then 0 times any vector is a 0 vector, and the 0 vector is collinear with b,
But there is no guarantee that vector a and vector b are collinear
If there's anything you do n' t understand, keep asking,

Parsing:
Your question is wrong.
Should be vector b and vector a collinear, b=ka, why k is not equal to 0
Because k =0, then 0 times any vector is a 0 vector, and the 0 vector is collinear with b,
But there is no guarantee that vector a is collinear with vector b
If there's anything you do n' t understand, keep asking,

△The lengths of the opposite sides of the three internal angles A, B and C of ABC are a, b and c respectively. Let the vector P=(a+c, b), Q=(b−a, c−a), if P∥ Q, the size of angle C is ______.