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How to multiply two vectors?
= Product of moduli of two vectors × cos angle
= Abscissa product + ordinate product
Multiplication formula of two vectors
A vector (A, B) B vector (C, D) A vector * B vector = AC+BD
Note whether you are asking for point multiplication or cross multiplication
A vector (A, B) B vector (C, D) A vector * B vector = AC+BD
Pay attention to whether you are asking for point multiplication or cross multiplication
An Algorithm for Multiplying Two Vectors
A vector (x, y) b vector (a, b)
A* b=ax+by
I know a*b=|a||b|cosθ, but a*b*c=? And who is cosθ multiplied? Is it |a||b||c|cosθ? What is the angle between two vectors? What should be the formula for multiplying three vectors? I know a*b=|a||b|cosθ, but a*b*c=? And who is cosθ multiplied is |a||b||c|cosθ? What is the angle between two vectors? What should be the formula for multiplying three vectors?
The result of multiplying two vectors is a number
The result of multiplying three vectors is a vector
So, if I give you the abc vector
Let you calculate the product, abc, acb, the result of the commutative operation is different,
Well, if we're going to do this, we' re going to start with the first two, and then we're going to get a number that's the coefficient of the next vector
What is the meaning of vector multiplication There's a lot of vector multiplication. So, vector multiplication is What does it mean?
Pointwise multiplication, also called the inner product and the quantity product of a vector. As the name implies, the result obtained is a number. Vector a. Vector b=|a||b|cos. In physics, given the force and displacement to work, is actually to find the inner product of vector F and vector s, that is, to use pointwise multiplication.
The definition of dot-multiplication is vector a·vector b=|a||b|cos, that the projective of a vector on the other vector is multiplied by the other vector.
How to do vector multiplication
For example: vector a=(m, n), vector b=(p, q)
Vector a×vector b=m×p+n×q (sum of abscissa and ordinate)
Alternatively, vector a× vector b=module of vector a×module of vector b×cosθ(θ is the angle between two vectors)
RELATED INFORMATIONS
- 1. What is the meaning of multiplying two vectors in a plane? When two scalars are multiplied, we know how many and what are added. And what does it mean to multiply two vectors? What's the point of production? What is the meaning of multiplying two vectors in a plane? When two scalars are multiplied, we know how many and what are added. And what does it mean to multiply two vectors? What's the point of being productive? What is the meaning of multiplying two vectors in a plane? When two scalars are multiplied, we know how many and what are added. And what does the multiplication of two vectors mean? What's the point of production?
- 2. What is the cross multiplication formula of three vectors? For example, A vector cross by B vector cross by C vector
- 3. What is a slip vector and what is a free vector
- 4. If a and b are mutually negative vectors, then a-b=, a+b=
- 5. Known A =(1,1), and A and A+2 B in the same direction, A• B.
- 6. Why is the vector multiplication negative? This is a coordinate multiplication problem Isn't vector multiplication a length? How can there be negative numbers?
- 7. It is known that the angles of the vectors a, b, c are equal, and the moduli of a, b, c are 1,2,3 respectively. It is known that the angles of the vectors a, b, c are equal, and the modules of a, b, c are 1,2,3, respectively.
- 8. Is the module of an equal vector equal
- 9. Vector a, b, c has the same starting point,|a|=|b|=2, ab=-1,(a-c, b-c)=60 degrees,|a-c|=Root 7, then the included angle of vector a, c is The vector a, b, c has the same starting point,|a|=|b|=2, ab=-1,(a-c, b-c)=60 degrees,|a-c|=Root 7, then the included angle of vector a, c is The vector a, b, c the same starting point,|a|=|b|=2, ab=-1,(a-c, b-c)=60 degrees,|a-c|=Root 7, then the included angle of vector a, c is
- 10. Given that the point G is the center of gravity of the triangle ABC, make a straight line through G on both sides of AB and AC and intersect at M and N respectively, and vector AM=x, vector AN=y vector AC, Find the value of 1/x+1/y Given that the point G is the center of gravity of the triangle ABC, the straight line passing through G intersects the two sides of AB and AC at M and N respectively, and the vector AM=x, the vector AN=y vector AC, Find the value of 1/x+1/y
- 11. λ,μ Are real numbers, if λa=μb, then a and b are not collinear. When λ=μ=0, a and b can be arbitrary vectors, satisfying λa=μb. How to understand this sentence
- 12. A vector is equal to (n+2, n^2-cosa^2), b vector is equal to (m,2/m+sina), where n, m, a are real numbers. If vector a=2 vector b, calculate the value range of n/m Cosa^2 is the square of cosa A vector is equal to (n+2, n^2-cosa^2), b vector is equal to (m,2/m+sina), where n, m, a are real numbers. If vector a=2 vector b, find the value range of n/m Cosa^2 is the square of cosa
- 13. Given vector a, b satisfies |a|=|b|=1, real number m, n satisfies m^2+n^2=1, then the value range of |ma+nb| is |Ma+nb ma nb 2(m^2+n^2)
- 14. Let e1, e2 be two non-collinear vectors, vector AB=2e1+ke2, vector CB=e1+3e2, vector CD=2e1-e2, if A, B, D are collinear, find the value of k
- 15. Let two vectors e1, e2 satisfy |e1|=2,|e2|=1, e1, e2 have an angle of 60 degrees, if the angle between vector 2te1+7e2 and vector e1+te2 is obtuse, Value range of factor t
- 16. The module of vector a=3, the module of vector b is equal to 4, and the positional relationship between vector a+3/4b and vector a-3/4b is The square of the module of (a+3/4b)×(a-3/4b)= a is equal to 0, so the position relation of the vector a+3/4b and a-3/4b is vertical. But the vector multiplication should not be the module of a+3/4b × the module of a-3/4b × the COS of their included angle. Besides, if the square difference is equal to zero, why are they vertical?
- 17. The basic theorem of collinear vector is that if a=0, then the necessary and sufficient condition of the collinear vector b and a is that there exists a unique real number λ such that b=λa. For example, if λ is equal to 0, then any two vectors are collinear. This is obviously not correct, because it does not satisfy a//b. Theorem. If I understand it in this way, then it is not a necessary and sufficient condition. What is the unique real number λ? Is λ=0 saying the particularity of collinear vector? For example, if λ=0, then b=0. In addition, if b=0, then λ=0. But it is strange because when λ=0, b=0, b (zero vector) and a (non-zero vector) are collinear, does this satisfy a//b of parallel vector?
- 18. 0
- 19. If e1 and e2 are a set of substrates in the plane, the following four sets of vectors can be used as the substrates of the plane vector: A, e1-e2, e2-e1B,2e1-e2, e1-1/2e2C,2e2-3e1,6e1-4e2D, e1+e2, e1-e2 If e1, e2 are a set of bases in the plane, the following four sets of vectors can be used as the bases of the plane vector: A, e1-e2, e2-e1B,2e1-e2, e1-1/2e2C,2e2-3e1,6e1-4e2D, e1+e2, e1-e2
- 20. Is any non-zero vector parallel to the unit vector