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The vector a=(cosα, sinα), b=(cosβ, sinβ),0<β<α If |a-b|=root2 find a perpendicular b let c=(0,1) if a+b=c find the value of The vector a=(cosα, sinα), b=(cosβ, sinβ),0<β<α If |a-b|=rootoot 2, find a perpendicular b Let c=(0,1) If a+b=c, find the value of
Solution (1) a-b=(cosa-cosb, sina-sinb)/a-b/=√(cosa-cosb)2+(sina-sinb)2=√1+1-2 cosacosb-2 sinasinb=√2 2-2 cosacosb-2 sinasinb=2 cosacosb+sinasinb=0, i.e. a*b=0 a⊥b (2) a+b=(cosa+cosb, sina+sinb) a+b=c=(0,1...
Known vector A=(sinθ,-2) and B=(1, cosθ) perpendicular to each other, where (0,π 2). To: (1) Values of sinθ and cosθ (2) The value of tanθ. Known vector A=(sinθ,-2) and B=(1, cosθ) perpendicular to each other, where (0,π 2). Request: (1) Values of sinθ and cosθ (2) The value of tanθ.
(1) By vector
A=(sinθ,-2) and vector
B=(1, cosθ) perpendicular to each other,
We get sinθ-2cosθ=0, and sin2θ+cos2θ=1, where (0,π
2),
Solution: sinθ=2
5
5, Cos θ=
5
5;
(2) By tanθ=sinθ
Cosθ, then tanθ=2.
(1) By vector
A=(sinθ,-2) and vector
B=(1, cosθ) perpendicular to each other,
We get sinθ-2cosθ=0, and sin2θ+cos2θ=1, where (0,π)
2),
Solution: sinθ=2
5
5, Cos θ=
5
5;
(2) By tanθ=sinθ
Cosθ, then tanθ=2.
The problem of the product of the number of vectors. Why is a. b. the same as b. a? A.b={ a }{ b }.cosθ B.a={ b }{ a }.cosθ {B }.cosθ{ a }.cosθ denotes the projection of b on a and the projection of a on b, respectively. Isn't the projection of b on a different from the projection of a on b? How can a.b. and b.a be equal in this way? Thank you. The problem of the product of the number of vectors. Why is a. b. the same as b. a? A.b={ a }{ b }.cosθ B.a ={ b }{ a }.cosθ {B }.cosθ{ a }.cosθ denotes the projection of b on a and the projection of a on b, respectively. Isn't the projection of b on a different from the projection of a on b? How can a.b. and b.a be equal in this way? Thank you. The problem of the product of the number of vectors. Why is a. b. the same as b. a? A.b={ a }{ b }.cosθ B.a ={ b }{ a }.cosθ {B }.cosθ{ a }.cosθ denotes the projection of b on a and the projection of a on b, respectively. Isn't the projection of b on a different from the projection of a on b? How can a.b. and b.a. be equal? Thank you.
Understand by the definition of quantity product
What is the relationship between the product of the number of |vector a and vector b| and |a||b| Why? What is the relationship between the product of the number of |vector a and vector b| and |a||b| Why? Why? What is the relationship between the product of |vector a and vector b| and |a||b| Why?
|Ab a||b|
Because ab=|a||b|cosθ
Given the coordinates of vectors a, b, how to find their product of quantities For example, vector a=(2 cosx,1), vector b=(cosx,√3s in 2x), find vector a·vector b Wait for the answer online
Corresponding coordinate multiplication is the quantity product, which is 2cosx*cosx+1 3s in 2x=1+2cos2x 3s in 2x
Given vector a=(0,3) vector b=(-4,4), then the product of the quantities of vectors a, b is? If vector a=(0,3) vector b=(-4,4), then the number product of vectors a, b is? If vector a=(0,3) vector b=(-4,4), then the product of vectors a and b is?
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RELATED INFORMATIONS
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- 7. Point A (-1,0) B (1,4) satisfies vector PA·vector PB=4, and the trajectory equation of point P is obtained. If the point Q is a symmetric point of P with respect to the straight line y=2(x-4), find the trajectory equation of the moving point Q Point A (-1,0) B (1,4) satisfies the vector PA·vector PB=4, and the trajectory equation of point P is obtained. If the point Q is a symmetric point of P with respect to the straight line y=2(x-4), find the trajectory equation of the moving point Q
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- 18. For the vector a, b, c and the real number λ, is the true proposition () in the following propositions possible to analyze these four in detail? A. If a*b=0, then a=0 or b=0 B. If λa=0, then λ=0 or a=0 C. If a^2= b^2, then a = b or a =-b D. If a*b=a*c, then b=c For the vector a, b, c, and real number λ, could the following real proposition () analyze these four in detail? A. If A*B=0, then A=0 or B=0 B. If λa=0, then λ=0 or a=0 C. If A2= B2, then A = B or A = B D. If a*b=a*c, then b=c
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