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AM is known that AM is the center line on BC in triangle ABC, and the vector method is used to prove that: AM^2=1/2(AB^2+AC^2)-BM^2 AM is known to be the median line on BC in triangular ABC, and the vector method is used to prove that: AM^2=1/2(AB^2+AC^2)-BM^2
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How to prove 4-point coplanar by vector method? Tell you four point coordinates, how to use vector method to prove their coplanar?
Four points can be connected by three lines. Let these three vectors be A, B and C respectively
As long as the vector C can be expressed as C = mA + nB, it can be proved that the four points are coplanar.
Four points can be connected by three lines. Let these three vectors be A, B and C respectively
As long as the vector C can be expressed as C=mA+nB, it can be proved that the four points are coplanar.
Proving Pythagorean Theorem by Vector Method
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The proof of high-grade vector method In the right triangle ACB, AD is the height on the oblique side BC, and the vector method is used to prove that the square of AD=BD·DC The proof of high school vector method In the right triangle ACB, AD is the height on the oblique edge BC, and the vector method is used to prove that the square of AD=BD·DC The proof of high school vector method In the right triangle ACB, AD is the height on the oblique side BC, and the vector method is used to prove that the square of AD=BD·DC
AB=AD+DBAC=AD+DC=AD+DC Because AB⊥AC, AB*AC=0 i.e.(AD+DB)*(AD+DC)=0 AD*AD+AD*DB+AD*DC+AD*DC+DB*DC=0 Because AD⊥DB, AD⊥DC, AD*DB=AD*DC=0. The above expression becomes AD*AD+DB*DC=0 i.e. AD*AD=-DB*DC=BD*DC.(All the above are directivity operations)...
Mathematical vector proof When the angle of vector a, vector b and vector c is 0 degree, then is |vector a+vector b+vector c|=|vector a vector b vector c|? If so, please certify The difference is 180 degrees. Mathematical vector proof When the angle of vector a, vector b and vector c is 0 degree, then is |vector a+vector b+vector c|=|vector a vector b vector c|? If so, please certify The different directions are 180 degrees.
It holds when vector a. vector b. vector c. forms an angle of 0 degrees
Then b=ma, c=na, and m, n >0, therefore
Left=|a+b+c|=|a+ma+na|=|(1+m+n) a|=(1+m+n)|a|
Right=|a b c|=|a ma na|=|a m|a n|a|
The distribution rate multiplied by the number, then left = right
Therefore the proposition holds.
How to Use Vector to Prove Mathematical Problems In the parallelogram ABCD, the point M is on the extension line of AB, and BM=1/2AB, the point N is on BC, and BN=1/3BC. How to Use Vector to Prove Mathematical Problems In the parallelogram ABCD, the point M is on the extension of AB, and BM=1/2AB, the point N is on BC, and BN=1/3BC.
Let MB=a, BN=b,
So vector
MD == MA + AD ==3 a +3 b ==3(a + b)==3*(MB + BN)==3 MN
Therefore, the MND three points are collinear
Let MB=a, BN=b,
So vector
MD == MA + AD ==3 a +3 b ==3(a + b)==3*(MB + BN)==3 MN
So, MND three-point collinear
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