The Proof of Four-Point Coplanar of Space Vector If ABC three points are not collinear, take any one point P to prove ABCP four points are collinear. There must be a clear process! The Proof of Four-Point Coplanar of Space Vector If ABC three points are not collinear, any point P is taken to prove ABCP four points are collinear. There must be a clear process! The Proof of Four-Point Coplanar of Space Vector If ABC three points are not collinear, take any point P to prove ABCP four points are collinear. There must be a clear process!

The Proof of Four-Point Coplanar of Space Vector If ABC three points are not collinear, take any one point P to prove ABCP four points are collinear. There must be a clear process! The Proof of Four-Point Coplanar of Space Vector If ABC three points are not collinear, any point P is taken to prove ABCP four points are collinear. There must be a clear process! The Proof of Four-Point Coplanar of Space Vector If ABC three points are not collinear, take any point P to prove ABCP four points are collinear. There must be a clear process!

You're wrong. It's probably ABCP.
The Problem of Transforming Four-Point Coplanar into Non-coplanar Two-vector Coplanar by Vector Method
1 4 Points constitute 2 straight lines parallel
2 With 3 points collinear
3 2 Vectors collinear consisting of 4 points
Meet any condition

You're wrong. I think you' re trying to prove ABCP is coplanar.
The Problem of Transforming Four-Point Coplanar into Non-coplanar Two-vector Coplanar by Vector Method
1 4 Points constitute 2 straight lines parallel
2 With 3 points collinear
3 2 Vectors collinear consisting of 4 points
Meet any condition

You've got the wrong question. It's to prove that the four points of ABCP are coplanar.
The Problem of Transforming Four-Point Coplanar into Non-coplanar Two-vector Coplanar by Vector Method
1 4 Points constitute 2 straight lines parallel
2 With 3 points collinear
3 2 Vectors collinear consisting of 4 points
Meet any condition

Let a, b, c be three vectors and prove that a, b, c are coplanar if and only if a+b, b+c, c+a are coplanar.

Let K1(a+b)+K2(b+c)+K3(c+a)=0, then (K1+K3) a+(K1+K2) b+(K2+K3) c=0, if a+b, b+c, c+a are coplanar, then (K1+K3),(K1+K2),(K2+K3) are not simultaneously 0, then K1, K2, K3 are not simultaneously 0(known by solving the equation system), so a, b, c are coplanar. The above parts are reversible, so a, b, c are coplanar.

The vector method is used to prove that the diagonal of a space quadrilateral is perpendicular to each other if and only if the sum of squares of opposite sides is equal.

为方便,下面#后的代表向量.#CD=#BD-#BC,#AC=#BC-#BA,#AD=#BD-#BA.对角线的点积:#AC·#BD=(#BC-#BA)·#BD=#BC·#BD-#BA·#BD 两组对边平方和分别为:AB2+CD2=AB2+(#BD-#BC)2=AB2+BD2+BC2-2#BD·#BC AD2+BC2=(#BD-#BA)2...

It is proved by vector that the sum of squares of two diagonals of parallelogram is equal to the sum of squares of quadrilateral.

Let AB = vector a, BC = vector b in parallelogram ABCD
Then vector CD = vector -a, vector DA = vector -b
Then vector AC = vector a+b, vector BD = vector b-a
Vector AC2+vector BD2=vector a2+2vector avector b+vector b2+vector a2-2vector avector b+vector b2
|Vector AC|2+|Vector BD|2=2|Vector a|2+2|Vector b|2
I.e. AC2+BD2=AB2+BC2+AD2+CD2
Come up or see, there's no way, there's no vector sign

Using Vector Method to Prove that the Square Sum of Two Diagonal Lines on Four Parallel Edges is Equal to the Square Sum of Four Edges Thank you, sir.

Let AB=a, AD=b (both vectors) be two adjacent sides of a parallelogram, then AC=a+b, DB=a-b,
Sum of squares of two diagonals =(a+b)2+(a-b)2=a2+b2+a2+b2= sum of squares of four sides

It is proved by vector that the sum of squares of two diagonals of parallelogram is equal to the sum of squares of parallelogram? Explain, the symbol should let the person know.

Let AB = vector a, BC = vector b, CD = vector - a, DA = vector - b, AC = vector a+b, BD = vector b-a, AC2+ vector BD2= vector a2+2, a, b+ vector b2+ vector a2-2, a, b+ vector b...

Let AB=vector a, BC=vector b, CD=vector-a, DA=vector-b, AC=vector a+b, BD=vector b-a, AC2+vector BD2=vector a2+2, a, b+vector b2+vector a2-2, a, b+vector b...