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Is the addition of two vectors the addition of two vectors?
The addition of two vectors is calculated according to the parallelogram rule: the starting points of the two vectors to be added are coincident, and the two vectors are taken as the adjacent sides of the parallelogram. The diagonal line from the starting points of the two vectors to the diagonal line is the combined vector, and the direction is from the starting points of the two vectors to the diagonal line. The module of the vector is the quantity, and the two directions are...
The addition of two vectors is calculated according to the parallelogram rule: the starting points of the two vectors to be added are coincident, and the two vectors are taken as the adjacent sides of the parallelogram. The diagonal line from the starting point of the two vectors to the diagonal line is the combined vector, and the direction is from the starting point of the two vectors to the diagonal line. The module of the vector is the quantity, and the two directions are...
Let vectors a and b be two non-zero non-collinear vectors 1. Write vector OA=a, vector OB=tb, vector OC=1/3(a+b), then what is the value of real number t, ABC three points are collinear? 2. If |a|=|b|=1, and the angle between a and b is 120°, then what is the value of |a-xb|? Let vectors a, b be two non-zero vectors that are not collinear 1. Write vector OA=a, vector OB=tb, vector OC=1/3(a+b), then what is the value of real number t, ABC three points are collinear? 2. If |a|=|b|=1, and the angle between a and b is 120°, then what is the value of |a-xb|?
1. OC=(1/3) OA+(1/3t) OB.
ABC three-point collinear→(1/3)+(1/3t)=1→t=1/2
2.(A-xb)2=1+x2-2x (-1/2)=x2+x+1=(x+1/2)2+3/4
When x=-1/2,|a-xb|=√3/2 is the minimum value.
Suppose vector a, vector b is two non-collinear non-zero vectors, the value of t is all real numbers, if vector a, the starting point of vector b is denoted by o, when t is what value, three... Suppose vector a, vector b is two non-zero non-collinear vectors, the value of t is all real numbers, if vector a, the starting point of vector b is denoted by o, when t is what value, the end point of three vectors a, tb,1/2(a+b) is on the line? Let vector a, vector b be two non-collinear non-zero vectors, the value of t is all real numbers, if vector a, the starting point of vector b is recorded as o, when t is what value, three... Suppose vector a, vector b is two non-zero non-collinear vectors, the value of t is all real numbers, if vector a, the starting point of vector b is denoted by o, when t is what value, the end point of three vectors a, tb,1/2(a+b) is on the line? Let vector a, vector b be two non-collinear non-zero vectors, the value of t is all real numbers, if vector a, the starting point of vector b is recorded as o, when t is what value, three... Suppose vector a, vector b is two non-zero non-collinear vectors, the value of t is all real numbers, if vector a, the starting point of vector b is denoted by o, when t is what value, the end point of three vectors a, tb,1/2(a+b) is on the straight line?
Let three vectors be A, B, C,
Then vector BA=a-tb, vector CA=a-1/2(a+b)=a/2-b/2,
The end points A, B, C are in line,
Then vector BA is parallel to CA,1/(1/2)=-t/(-1/2),(corresponding coefficient ratio is equal)
T =1.
Let three vectors be A, B, C,
Then vector BA=a-tb, vector CA=a-1/2(a+b)=a/2-b/2,
End points A, B, C are on the straight line,
Then vector BA is parallel to CA,1/(1/2)=-t/(-1/2),(corresponding coefficient ratio is equal)
T =1.
Is the product formula of the vector the sum of the products of the coordinates?
Given three points A (4,-2) B (-4,4) C (1,1), find the unit vector whose direction is consistent with vector AB
Vector AB=(-8,6)
|AB |=10,
The unit vector whose direction is consistent with the vector AB is AB/|AB|=1/10*(-8,6)=(-4/5,3/5).
The unit vector whose direction is opposite to vector AB is -AB/|AB|=-1/10*(-8,6)=(4/5,-3/5).
Let vector a, b be non-zero and vector b be non-parallel. Let vector a, b be non-zero vector and vector b be non-parallel.
Proving that the two vectors are assumed to be parallel
Then a-b=n (a+2b)
A-b=na+2nb
(N-1) a+(2n+1) b=0
So n-1=0 and 2n+1=0
So n=1 and n=-1/2
Apparently, the above formula doesn't work.
So n does not exist,
Therefore, a-b is not parallel to a+2b
Note: ab above is a vector
Proving that the two vectors are assumed to be parallel
Then a-b=n (a+2b)
A-b=na+2nb
(N-1) a+(2n+1) b=0
So n-1=0 and 2n+1=0
So n=1 and n=-1/2
Apparently, that doesn't work.
So n does not exist,
Therefore, a-b is not parallel to a+2b
Note: ab above is a vector
Proving that the two vectors are assumed to be parallel
Then a-b=n (a+2b)
A-b=na+2nb
(N-1) a+(2n+1) b=0
So n-1=0 and 2n+1=0
So n=1 and n=-1/2
Apparently, the above formula doesn't work.
So n does not exist,
Therefore, a-b is not parallel to a+2b
Note: ab above are all vectors
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