![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
Given vectors a, b, and vectors AB=a-10b, BC=-5a+6b, CD=7a-2b, the three points of a certain collinear are Given vectors a, b, and vectors AB=a-10b, BC=-5a+6b, CD=7a-2b, the three points of certain collinearity are
Three-point collinear means that the vector is proportional
AC=AB+BC=-4a-4b
BD=BC+CD=2a+4b
It can be seen that AB, BC, AC, CD and BD are out of proportion
Therefore, there are no three points collinear in these four points
Three-point collinear means that the vector is proportional
AC=AB+BC=-4a-4b
BD=BC+CD=2a+4b
It can be seen that AB, BC, AC, CD and BD are out of proportion
Therefore, there are no three collinear points in these four points
The known vector a=(sinθ,-2) is perpendicular to b (1, cosθ), where (0.π/2) 1. Find the values of sinθ and cosθ 2. If sin (θ-ψ)= tenth root +,0<ψ<π/2, find the value of cosψ. The vector a=(sinθ,-2) is known to be perpendicular to b (1, cosθ), where (0.π/2) 1. Find the values of sinθ and cosθ 2. If sin (θ-ψ)= tenth root +,0<ψ<π/2, find the value of cosψ.
1.(-2/Sinθ)(cosθ/1)=-1sinθ=2cosθsin2θ+cos2θ=1(2cosθ)2+cos2θ=15cos2θ=1cos2θ=1/5(0.π/2), cosθ>0cosθ=√5/5sinθ=2√5/52.0<ψ<π/2 cosψ>0sin (θ-ψ)=√...
Is the zero vector a parallel vector, a collinear vector? Don't parallel vectors mean non-zero vectors
The zero vector is parallel to any vector. Parallel vectors are collinear.
If that vector a. b is two non-collinear vector with the same starting point, Ask if there is a real t so that the end points of the three vectors a, tb.1/3(a+b) are on the same line? If yes, the real number t is requested. If no, please explain the reason. Answer t =1, If that vector a. b is a non-zero vector with the same starting point, Ask if there is a real t so that the end points of the three vectors a, tb.1/3(a+b) are on the same line? If yes, the real number t is requested. If no, please explain the reason. Answer t =1, If that vector a. b is a non-zero vector with two non-collinear, Ask if there is a real t so that the end points of the three vectors a, tb.1/3(a+b) are on the same line? If yes, the actual number t is requested. If no, please explain the reason. Answer t =1,
A, tb,1/3(a+b) has the same starting point, assuming the end point is on the same straight line,
Let three vectors be A, B, C,
Then vector BA=a-tb, vector CA=a-1/3(a+b)=2a/3-b/3, vector BA is parallel to CA,
1/(2/3)=-T/(-1/3),
T =1/2
A, tb,1/3(a+b) have the same starting point, assuming the end point is on the same straight line,
Let three vectors be A, B, C,
Then vector BA=a-tb, vector CA=a-1/3(a+b)=2a/3-b/3, vector BA is parallel to CA,
1/(2/3)=-T/(-1/3),
T =1/2
Coordinate representation of space vector a//b? Coordinate representation of spatial vector a//b?
0
Given A (0,3), B (2,0), C (-1,3), and AB+2 The unit vector with the opposite AC direction is () A.(-1,1) B.(0,-1) C.(0,1) D.(1,-1) Given A (0,3), B (2,0), C (-1,3), and AB+2 The unit vector in the opposite direction of AC is () A.(-1,1) B.(0,-1) C.(0,1) D.(1,-1)
0
RELATED INFORMATIONS
- 1. What is the known vector |a|=2|, b|=3|a-2b|=5|a+2b|?
- 2. In the spatial rectangular coordinate system O-xyz, the normal vector of the plane OAB is A =(2,-2,1), if P (-1,3,2) is known, then the distance from P to the plane OAB is equal to () A.4 B.2 C.3 D.1
- 3. Given vector a=(2,0), b is a nonzero vector, if the angle between a+b, a-b and the positive direction of x axis is (∏/6) and (2∏/3), then b=
- 4. If the vectors a and b are not collinear, a·b=0, and c=a-(a·a)/(a·b) b, what is the included angle between vectors a and c This equation can be directly calculated c=0 ah, why there is the assumption of c=0? Doesn't a.a.b/a.b equal a? A-a is equal to zero. Ask for answers! Thank you! If vectors a and b are not collinear, a·b=0, and c=a-(a·a)/(a·b) b, then what is the angle between vectors a and c This equation can be directly calculated c=0 ah, why there is the assumption of c=0? Doesn't a.a.b/a.b equal a? A-a is equal to zero. Ask for answers! Thank you!
- 5. Given vector a=(2,1), vector b=(-8,6) (1) Given vector a=(-1,2), vector b=(1,-2), find the coordinates of vector a+vector b, vector a-vector b,2 vector a-3 vector b. (2) Given vector a=(2,1), vector b=(-8,6), vector c=(4,6), find 2 vector a+5 vector b-vector c, and express the vector with base vector i, j
- 6. Given points A (6,1), B (1,3) C (3,1), the projection of vector AB on vector BC is _____?
- 7. Three vertices A (0,2), B (-1,-2), C (3,1) of a quadrilateral ABCD are known, and BC =2 AD, the coordinates of vertex D are () A.(2,7 2) B.(2,−1 2) C.(3,2) D.(1,3) Three vertices A (0,2), B (-1,-2), C (3,1) of the quadrilateral ABCD are known, and BC =2 AD, the coordinates of vertex D are () A.(2,7 2) B.(2,−1 2) C.(3,2) D.(1,3)
- 8. If two vectors parallel to the same vector are collinear vectors, the answer is right. If the same vector is zero, how to explain?
- 9. Why can the matrix rank of row vector multiply column vector be less than or equal to 1?
- 10. Formulas of Two Vectors Parallel
- 11. Known vector A, B, and AB = A+2 B, BC=-5 A+6 B, CD =7 A-2 B, must be collinear () A.A, B, D B.A, B, C C.B, C, D D.A, C, D Known vector A, B, and AB = A+2 B, BC=-5 A+6 B, CD =7 A-2 B, then certain collinear () A.A, B, D B.A, B, C C.B, C, D D. A, C, D
- 12. Given ABCD is any four points on the plane, then vector AB + vector CD + vector DA =?
- 13. Vector a=(2,4), vector b=(1,1), vector b⊥(vector a+n vector b), then n=?
- 14. Given vector a=(-1,1), b=(-3,-2), find (b-a)×(b+a)
- 15. Known vector A =(3,2), B =(x,4) and A∥ B, the value of x is () A.-6 B.6 C.8 3 D.-8 3
- 16. O is the inner triangle if and only if aOA vector + bOB vector + cOC vector =0 vector.
- 17. The Proof of Four-Point Coplanar of Space Vector If ABC three points are not collinear, take any one point P to prove ABCP four points are collinear. There must be a clear process! The Proof of Four-Point Coplanar of Space Vector If ABC three points are not collinear, any point P is taken to prove ABCP four points are collinear. There must be a clear process! The Proof of Four-Point Coplanar of Space Vector If ABC three points are not collinear, take any point P to prove ABCP four points are collinear. There must be a clear process!
- 18. What Is the Necessary and Sufficient Condition for Linear Independence of n-dimensional Column Vector What is the Necessary and Sufficient Condition for Linear Independence of n-dimensional Column Vector
- 19. Vector Proving Problem (λa)·b=λ(a·b)=a·(λb) Two Proofs of Vector Algorithm (λA)·b=λ(a·b)=a·(λb) A·b=a·ca⊥(b-c)
- 20. 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