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Excuse me: vector multiplied by a non-zero vector equal to the zero vector?
High School: The product of a vector multiplied by a vector is a quantity product, so a zero vector multiplied by a non-zero vector equals zero!
In university: the product of a vector and a vector is divided into an inner product and an outer product. The inner product is the product of quantities, and the outer product is the zero vector multiplied by a non-zero vector.
Given vector a=(-1,2,3), vector b=(1,1,1), then the projective length of vector a on vector b is?
A.b=-1*1+1*2+1*3=4;
The projection of vector a on vector b = a.b/|b|=4/ root number 3;
The projective length of vector a on vector b =4/ root number 3;
Prove: vector AB•CD+BC•AD+CA•BD=0
0
Let vector a and vector b be two non-collinear non-zero vectors (t∈R) (1) If vector OA=vector a, vector OB=tvector b, vector OC=1/3(vector a+vector b), then what is the value of real number t, A, B and C are collinear? (2) If vector a = vector b =1 and the angle between vector a and vector b is 120°, then what is the value of vector a-x vector b? There's only one answer.
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If a, b are two non-collinear nonzero vectors, t belongs to R. (1) If the starting points of a and b are the same, what is the value of t? (2) If |a|=|b| and the angle between a and b is 60°, what is the value of t? If a, b are two non-collinear nonzero vectors, t belongs to R. (1) If the starting points a and b are the same, what is the value of t, a, tb,(a+b)/3 The end point of the three vectors is on the straight line? (2) If |a|=|b| and the angle between a and b is 60°, what is the value of t?
Let vector OA=a, OB=tb, OC=1/3(a+b), if the terminal point of the three vectors is on a straight line, there must be a vector AC=mAB, where m is a real number, vector AC=OC-OA=(b-2a)/3, vector AB=tb-a, then there is (b-2a)/3=m (tb-a), and the corresponding coefficient is proportional.
What is the vector a multiplied by vector b? What is the vector a multiplied by the vector b?
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RELATED INFORMATIONS
- 1. Given the points A (1,3), B (4,-1), then the vector The unit vector of AB in the same direction is ______. Given points A (1,3), B (4,-1), then the vector The unit vector of AB in the same direction is ______. Given the point A (1,3), B (4,-1), then the vector The unit vector of AB in the same direction is ______.
- 2. Is the addition of two vectors the addition of two vectors?
- 3. Is the zero vector in the same direction as the zero vector? Is the zero vector the same direction as any non-zero vector? Is the zero vector in the same direction as the zero vector? Is the zero vector the same as any non-zero vector?
- 4. Must two collinear vectors be the same or opposite? What if one of them is a zero vector?
- 5. The following propositions are true:1 The module of a vector is a positive real number 2 If two unit vectors are parallel to each other, the two unit vectors are equal... The following propositions are true:1 The module of a vector is a positive real number 2 If two unit vectors are parallel to each other then the two unit vectors are equal 3 If vector AB = vector CD then ABCD four points form a parallelogram The following propositions are true:1 The module of a vector is a positive real number 2 If two unit vectors are parallel to each other, then these two unit vectors are equal... The following propositions are true:1 The module of a vector is a positive real number 2 If two unit vectors are parallel to each other, then these two unit vectors are equal 3 If the vector AB = vector CD, then the ABCD four points form a parallelogram
- 6. If the vector a (1,1,0) is known, then the unit vector e is?
- 7. How to Judge the Pairwise Orthogonal of Vector Groups in Linear Algebra
- 8. 1. Given linear independence of n-dimensional vector a1a2... a (n-1), non-zero vector b is orthogonal to ai to prove a1,a2,a3...a (n-1), b is linear independence 2 The following vectors are organized into standard vector group a1=(1,-1,1) Ta2=(-1,1) Ta3=(1,1-1) T3 by Schmidt standard orthogonalization method Let a=(a1a
- 9. 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
- 10. State reasons 1. Given vector AB =2, vector CD =4, the angle between vector AB and vector CD is 60°, Find (1) vector AB+vector CD (2) Vector AB + angle between vector CD and vector AB State reasons 1. Given that vector AB =2, vector CD =4, the angle between vector AB and vector CD is 60°, Find (1) vector AB+vector CD (2) Vector AB + angle between vector CD and vector AB
- 11. Let α be n-dimensional column vector and E be n-order identity matrix. It is proved that A=E-2 T/( Tα) is an orthogonal matrix.
- 12. True or False: Vector a=(1,1) and vector b=(t,-t) must be parallel to each other. True or False: vector a =(1,1) and vector b =(t,-t) must be parallel to each other.
- 13. If any n-dimensional nonzero vector is the eigenvector of n-order matrix A, then A is a quantitative matrix If any n-dimensional nonzero vector is the eigenvector of n-order matrix A, then A is a quantity matrix
- 14. The constant 0 is multiplied by a non-zero vector equal to the zero vector, then the zero vector is multiplied by a non-zero vector equal to zero or zero vector
- 15. What is the modulus of a + b + c if the vectors a, b, c are two equal angles and the modulus of a is equal to 1, the modulus of b is equal to 1, the modulus of c is equal to 3? Just explain how it's equal to 2,5. What is the modulus of a + b + c if the two vectors a, b, c form equal angles and the modulus of a is equal to 1, the modulus of b is equal to 1, the modulus of c is equal to 3? Just explain how it's equal to 2,5.
- 16. What does vector multiplication equal to negative one mean?
- 17. Vector multiplication rule
- 18. Multiply two vectors Vector AC (a, b), Vector BC (c, d), AC·BC=?
- 19. If a is collinear with b, then there is a unique real number λ such that b=λa. Why is it wrong? (A, b are vectors)
- 20. If a=0, then vector b is collinear with a if and only if there is a unique real number λ, so that b=λa emphasizes the effect of a=0 If a =0, then the necessary and sufficient condition for the vector b to be collinear with a is that there is a unique real number λ, so that b =λa emphasizes the action of a =0