If the vectors a, b, c satisfy a+b+c=0, and /a/=3,/b/=1,/c/=4, then how much is a*b+b*c+c*a? Because /a/+/b/=/c/, and because a+b+c=0, a and b must be in the same direction direction, and c in the opposite direction. So a*b+b*c+c*a=/a//b/-/b//c/-/a//c/=3-4-12=-13 Find the reason why a and b must be in the same direction and c must be in the opposite direction. ——

If the vectors a, b, c satisfy a+b+c=0, and /a/=3,/b/=1,/c/=4, then how much is a*b+b*c+c*a? Because /a/+/b/=/c/, and because a+b+c=0, a and b must be in the same direction direction, and c in the opposite direction. So a*b+b*c+c*a=/a//b/-/b//c/-/a//c/=3-4-12=-13 Find the reason why a and b must be in the same direction and c must be in the opposite direction. ——

Because the sum of the two vectors is 0, the sum of the two vectors must be opposite to the third vector. The module of a is 3. b is 1, and the module of c is 4. So the sum of a and b vectors is equal to c (the module of c is larger). The two vectors of ab must be in the same direction, and the two vectors of ab and c are in the opposite direction. So the module of a vector times the module of b vector is a times the module of b...

Because the sum of and vectors is 0, the sum of two vectors (vectors) must be opposite to the third vector of equal magnitude. The module of a is 3. b is 1, and the module of c is 4. Therefore, the sum of vectors of a and b is equal to c (the module of c is larger). Inevitably, the two vectors of ab are in the same direction, and the two vectors of ab and c are in the opposite direction. So the module of a is multiplied by the module of b is multiplied by the module of b.

Because the sum vector is 0, is 0, the sum of the two vectors must be opposite to the third vector module of a is 3. b is 1, and the module of c is 4. So the sum of a and b vectors is equal to c (the module of c is larger). It is necessary that the two vectors are in the same direction, ab and c are in the opposite direction. So the module of a vector times the module of b vector is a times the module of b.

When the vector ab satisfies what condition |a-b|=|a||b|

0

Given a parallelogram ABCD, the position vectors of fixed points A, B, C, D with respect to any point O in the plane are denoted as a, b, c, d, respectively.

Vector CO=c Vector DO=d Vector BO=b Vector AO=a Vector OA=-a Vector OD=-d
Vector BO+vector OA=vector BA
Vector CO + Vector OD = Vector CD
Vector BA = Vector CD
Vector BO+vector OA=vector CO+vector OD
B+(-a)= c+(-d)
A+c=b+d

Given a parallelogram ABCD, its vertices A, B, C, D are denoted as a, b, c, d, respectively, relative to the position vector of any point O in the plane. Test a+c=b+d Given a parallelogram ABCD, its vertices A, B, C, D are denoted as a, b, c, d respectively with respect to the position vector of any point O in the plane. Test a+c=b+d

A = d + vector DA, c = b + vector BC
Because quadrilateral ABCD is a parallelogram, AD is parallel to BC
So vector DA = vector CB =-- vector BC, so vector DA + vector BC =0
A+c=(d+vector DA)+(b+vector BC)=b+d+(vector DA+vector BC)=b+d+0=b+d

In parallelepiped ABCD-A' B' C' D', vector AB = a, vector AD = b, vector AA'= c... M and N are two trisection points of D'B, and vector A' M and vector A'N are obtained. In parallelepiped ABCD-A' B' C' D', vector AB = a, vector AD = b, vector AA'= c... M and N are two trisection points of D' B, and vector A' M and vector A' N are obtained. In parallelepiped ABCD-A' B' C' D', vector AB=a, vector AD=b, vector AA'=c... M and N are two trisection points of D' B, and vector A' M and vector A' N are obtained.

(M close to B) A'M=A' D'+2D' B/3=b+(2/3)*(D'A'+A'A+AB)=b+(2/3)*(-b-c+a).
A'N=A' D'+D' B/3=b+(1/3)*(D'A'+A'A+AB)=b+(1/3)*(-b-c+a).

Quadrilateral ABCD, vector AB=vector a, vector BC=vector b, vector CD=vector d, vector DA=vector d, and a*b=b*c=c*d=d*a The final abcd is the vector, finding the shape of the quadrilateral ABCD Quadrilateral ABCD, vector AB=vector a, vector BC=vector b, vector CD=vector d, vector DA=vector d, and a*b=b*c=c*d=d*a The final abcd is a vector, finding the shape of the quadrilateral ABCD

Vector a point multiply vector b point multiply vector b point multiply vector c point multiply vector c point multiply vector d point multiply vector d point multiply vector a:-|a b cosDAB=-|b c|*cosABC=-|c d|*cosBCD=-|d a|*cosCDA to obtain cosDAB, cosABC, cosBCD, cosCD, cosCDA is the same sign in the quadrilateral the sum must be...