![](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 vector a =(4.3), vector B =(2,4) then cos =?
Cosine value = Vector inner product / Vector modular product =(4*2+3*4)/[ Srt (42+32)* Srt (22+42)]=2/ Srt5
(Sprt is the programming language, meaning square root)
What is the formula for the distance between two parallel planes in a vector?
A square + B square + C square | D1- D2| under the root sign. Note that the coefficients of the two planes must be the same to use this formula.
A square + B square + C square | D1-D2| under the root sign. Note that the coefficients of the two planes must be consistent to use this formula.
0
This is good to remember. Let two vector coordinates be (x1, y1, z1),(x2, y2, z2)(none of them are zero vectors).
1 Vertical is point multiplication to 0, just remember the definition of point multiplication: each coordinate component is multiplied and added. So the vertical formula is x1x2+y1y2+z1z2=0
2 Parallel is better to remember, that is, the corresponding coordinate components are proportional, x1: x2=y1: y2=z1: z2
Vector parallel, vertical formula
The two vectors a, b are parallel: a=λb (b is not a zero vector); the two vectors are vertical: the quantity product is 0, i.e. a•b=0
Coordinate representation: a=(x1, y1), b=(x2, y2)
A//b if and only if x1y2-x2y1=0
A⊥b if and only if x1x2+y1y2=0
Two vectors a, b b are parallel: a=λb (b is not a zero vector); the two vectors are vertical: the quantity product is 0, i.e. a•b=0
Coordinate representation: a=(x1, y1), b=(x2, y2)
A//b if and only if x1y2-x2y1=0
A⊥b if and only if x1x2+y1y2=0
If vector a=(3,-m) and vector B=(-2,1) are perpendicular, then M=how many? Find the formula to find the tutorial? If vector a =(3,-m) and vector B =(-2,1) are perpendicular, then M = how many? Find the formula for the tutorial?
Vector a is perpendicular to vector b
3×(-2)+(-M)×1=0
M=-6
PS: vector a=(x, y) is perpendicular to b=(m, n), then xm+yn=0
What conditions do vectors A and B satisfy so that a+b and a-b are perpendicular to each other
Parallel
RELATED INFORMATIONS
- 1. The condition that a vector plus b vector is perpendicular to a vector minus b vector is A vector =(x1, y1) B vector =(x2, y2)
- 2. In the right triangle ABC, the angle C =90°, AB =5, AC =4 Find the vector AB.BC? Product of quantity! Would you like to start here? In the right triangle ABC, the angle C =90°, AB =5, AC =4 Find the vector A B. BC? Product of quantity! Would you like to start here?
- 3. Given A (-2,4), B (3,-1) C (-3,-4) O as the origin of coordinates, let vector AB = vector a, vector BC = vector b, vector CA = vector c Given A (-2,4), B (3,-1), C (-3,-4). Let vector AB = vector a, vector BC = vector b, vector CA = vector c, and vector CM =3 vector c, vector CN =-2 vector b 1. Find 3a+b-3c 2. Satisfy a=mb+nc
- 4. On-line equal y=a*x^2b*xc AB, BC, CA composition ABC,AB BC CA =0 19.6 X 14.2 x 5.2 cm1n (MN)=1nM 1nM On-line equal y=a*x^2b*xc ternary AB, BC, CA composition ABC,AB BC CA =0 19.6 X 14.2 x 5.2 cm1n (MN)=1nM 1nM
- 5. Product of space vectors Find the volume of a =6,1,-2›, b =0,2,3›, c =6,-2,4› Is it the length of the fork of 3 vectors? Better give me an answer. I'm wrong.
- 6. Let x∈R vector a=(x,1) vector b=(1,-2) and vector a⊥ vector b, then | vector a vector b| equals | Vector a + Vector b | Let x∈R vector a=(x,1) vector b=(1,-2) and vector a⊥ vector b then | vector a vector b| equals | Vector a + Vector b |
- 7. The vector a is known to be equal to (-2.3).b=(5.x), and a⊥b. then x=? A=-15/2 b=-2 The vector a is known to be equal to (-2.3).b=(5.x), and a⊥b. then x=? A=-15/2b=-2/15c=10/3d=10/3 The vector a is known to be equal to (-2.3).b=(5.x) and a⊥b. then x=? A=-15/2 b=-2 The vector a is known to be equal to (-2.3).b=(5.x) and a⊥b. then x=? A=-15/2b=-2/15c=10/3d=10/3 The vector a is known to be equal to (-2.3).b=(5.x), and a⊥b then x=? A=-15/2 b=-2 The vector a is known to be equal to (-2.3).b=(5.x), and a⊥b then x=? A=-15/2b=-2/15c=10/3d=10/3
- 8. A Simple Calculation Using Vector Product → → → → → → → → May I ask why you (a-2b)(2a+b)=2a (^2)-2b (^2)-3a·b (^2) It means square. Thank you, little sister! Using Vector Product to Calculate Simply → → → → → → → → May I ask why the experts (A-2B)(2A+B)=2A (^2)-2B (^2)-3A·B (^2) It means square. Thank you, little sister!
- 9. Given vector a=(-1, root number three), try to find the unit vector n with an angle of 45 degrees of vector a Given the vector a=(-1, root number three), try to find the unit vector n with an angle of 45 degrees between the sum vector a
- 10. Given that i, j is the unit vector in the positive direction of x, y axis, let vector a=(x-root number 3) i+yj, vector b=(x+root number 3) i+yj, and satisfy direction |a||b|=4 Finding the Trajectory Equation of Point P (x, y) Given that i, j are unit vectors in the positive direction of x and y axes, let vector a=(x-root number 3) i+yj, vector b=(x+root number 3) i+yj, and satisfy direction |a||b|=4 Finding the Trajectory Equation of Point P (x, y)
- 11. In right triangle ABC, if vector A B =(1, k), vector AC =(2,1), and angle C is equal to ninety degrees, then the value of k
- 12. Given that the area S of triangle ABC satisfies that the root number 3 is less than or equal to S is less than or equal to 3, and the vector AB×vector BC=6, the included angle between vector AB and vector BC is a,
- 13. In triangle ABC, the opposite sides of angles A, B and C are a, b and c respectively, if the product of vector AB and vector AC is equal to the product of vector BA and vector BC and is equal to k (k is a real number) (1) Judge the shape of triangle ABC; (2) If c=√2, find the value of k. In triangle ABC, the opposite sides of angles A, B and C are a, b and c respectively, if the product of vector AB and vector AC is equal to the product of vector BA and vector BC and k (k is real) (1) Judge the shape of triangle ABC; (2) If c=√2, find the value of k.
- 14. Given vector a=(6,4), vector b=(3,8), and x multiplied by vector a+y multiplied by vector b=(-3,5), then x equals y equals Is it done with vector addition?
- 15. If a normal vector of the plane α is n=(4,1,1) and a direction vector of the straight line l is α=(-2,-3,3), then the sine value of the angle between l and α is
- 16. Find the plane equation of M (3,0,-2) with normal vector n=(-2,-4,3)
- 17. Given l, and the direction vector of l is (2, m,1), the normal vector of plane α is (1,1 2,2), Then m=______.
- 18. If the coordinate of vector p at base {abc} is (2010,2011,2012), then the coordinate of vector p at base {a, b+c, b-c} is? If the coordinates of vector p at base {abc} are (2010,2011,2012), then the coordinates of vector p at base {a, b+c, b-c} are?
- 19. In triangle ABC, A=∏/6, and (1+Root 3) c=2b (1) Find angle C (2) If the product of CB vector and CA vector is 1+Root 3, Find a, b, c In triangle ABC, A=∏/6, and (1+Root 3) c=2b (1) Find the angle C (2) If the product of CB vector and CA vector is 1+Root 3, Find a, b, c In triangle ABC, if A=∏/6 and (1+Root 3) c=2b (1), angle C (2) If the product of CB vector and CA vector is 1+Root 3, Find a, b, c
- 20. Vector a=(1,2), b=(1,-1), then /a+2b/=