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On the Formula of Vector
Parsing:
These formulas are more commonly used:
Let a and b be vectors
Then ab=|a||b|cos
If a is (x1, y1), b is (x2, y2)
Then |a|=√(x12+y12)|b|=√(x22+y22)
Ab=x1x2+y1y2
Vector formula 990,320° Long Length 8653,225° How long do the two vectors add up? How many degrees? And give me that formula, Vector formula Length 990,320° Length 8653,225° How long do the two vectors add up? How many degrees? And give me that formula, Vector formula Length 990,320° Length 8653,225° How long do the two vectors add up? How many times? And give me that formula,
Method 1:√[990 2+8653 2-2*990*8653*cos (180°-(320°-225°))]=√(980100+74874409-1493234.11)=√74361274.89(√ for root number) Formula √[ a2+b2-2ab*cos (180°-)].
What is the mathematical vector formula? Specific
1. Unit vector: unit vector a0=vector a/|vector a|
2. P (x, y) then vector OP=x vector i+y vector j
|Vector OP |= root sign (x square + y square)
3.P1(x1, y1) P2(x2, y2)
Then vector P1P2={ x2-x1, y2-y1}
| Vector P1P2|= root sign [(x2-x1) square +(y2-y1) square]
4. Vector a={ x1, x2} Vector b={ x2, y2}
Vector a* vector b=|vector a*|vector b|*Cosα=x1x2+y1y2
Cosα=vector a*vector b/|vector a*|vector b|
(X1x2+y1y2)
Root sign (x1 square + y1 square)* Root sign (x2 square + y2 square)
5. Space vector: Idem inference
(Tip: Vector a={ x, y, z})
6. Sufficient and necessary conditions:
If that vector a⊥ vector b
Then vector a* vector b=0
If vector a//vector b
Then vector a* vector b= vector a vector b|
Or x1/x2= y1/y2
7.|Vector a±Vector b|Square
=| Vector a| square +| vector b| square ±2 vector a* vector b
=(Vector a ± vector b) square
Given that O is any point in space, A.B.C.D satisfies that any three points are not collinear, but four points are coplanar, and vector OA=3x vector BO+4y vector CO+5z vector DO, then 3x+4y+5z=?
Let A, B and C be three non-collinear points. Then for any point P, there exists a unique ordered real array x, y, z such that the vector OP=x vector OA+y vector OB+z vector OC. If x+y+z=1, then P, A, B and C are coplanar. Then, according to the condition given by you, the answer is obviously 1 as a process.
Let A, B and C be three non-collinear points. Then for any point P, there exists a unique ordered real array x, y, z such that the vector OP=x vector OA+y vector OB+z vector OC. If x+y+z=1, then P, A, B and C are coplanar. Then, according to the condition given by you, the answer is obviously that 1 is a process.
Let A, B and C be three non-collinear points. Then for any point P, there exists a unique ordered real array x, y, z such that the vector OP=x vector OA+y vector OB+z vector OC. If x+y+z=1, then P, A, B, C are coplanar. Then, according to the condition given by you, the answer is obviously 1 as a process.
Given vectors a=(1,2), b=(1,0), c=(3,4) If the input is a real number,(a+input b)//c, then what is the input equal to Given vectors a=(1,2), b=(1,0), c=(3,4) a real number,(a+input b)//c, then what is the input equal to
A b =(1,2)+λ(1,0)=(1,2)+(λ,0)=(1+λ,2)
C=(3,4)
Because (a+in b)//c,
(1+λ)/3=2/4(Conditions of vector parallelism, i.e. proportional to coordinate)
Solution:λ=1/2
If A (3,5,-7), B (-2,4,3) is known, what is the projective length of vector AB on the coordinate plane yOz?
The projection of a point M (a, b, c) on the yoz plane is M1(0, b, c).
(Law: x=0, y, z invariant)
Therefore, the projection of A (3,5,7) and B (-2,4,3) is
A1(0,5,7), B1(0,4,3)
Therefore, the projection length is |A1B1|=
=Root number [(5-4)^2+(7-3)^2=Root number (17)
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