Given the plane vector a =(3,-1 under the root), b =(1/2,3/2 under the root). (1) If there are real numbers k and t, x=ta+(t^2-5t+1) b, y=-ka+ab, and x is perpendicular to y, find the relation k=f (t) (2) According to the conclusion of (1), try to find the minimum value of the function k=f (t) on t (0,4). Given the plane vector a =(3,-1 at root), b =(1/2,3/2 at root). (1) If there are real numbers k and t, x=ta+(t^2-5t+1) b, y=-ka+ab, and x is perpendicular to y, find the relation k=f (t) (2) According to the conclusion of (1), try to find the minimum value of the function k=f (t) on t belonging to (0,4).

Given the plane vector a =(3,-1 under the root), b =(1/2,3/2 under the root). (1) If there are real numbers k and t, x=ta+(t^2-5t+1) b, y=-ka+ab, and x is perpendicular to y, find the relation k=f (t) (2) According to the conclusion of (1), try to find the minimum value of the function k=f (t) on t (0,4). Given the plane vector a =(3,-1 at root), b =(1/2,3/2 at root). (1) If there are real numbers k and t, x=ta+(t^2-5t+1) b, y=-ka+ab, and x is perpendicular to y, find the relation k=f (t) (2) According to the conclusion of (1), try to find the minimum value of the function k=f (t) on t belonging to (0,4).

(1)
Vector a=(3,-1 at root), b=(1/2,3/2 at root).
|A|=2,|b|=1
A ●b=√3/2-√3/2=0
X=ta+(t^2-5t+1) b,
Y=-ka+b [here's the problem, the coefficient of b becomes 1]
X is perpendicular to y,
X ●y=0
I.e.[ ta+(t^2-5t+1) b ]●[-ka+b ]=0
-Tk|a|2+(t2-5t+1)|b|2+[ t-k (t2-5t+1) a●b=0
-4Tk+(t2-5t+1)=0
K =(t2-5t+1)/(4t)
(2)
K =1/4[ t+1/t-5](0

For the plane vector problem, if vector a=(3,1 under the root number) and vector b=(3,2 under the -2 root number), then the angle between vector a and vector b is? To process

Cosa=ab/(|a||b|)

What is the angle 180 degrees between the plane vector b and the vector a=(1,-2),|b|=3 roots 5, then b? Explain clearly, have a problem solving process, detailed What is the angle 180 degrees between the plane vector b and the vector a =(1,-2),|b|=3 roots 5, then b? Explain clearly, have a problem solving process, detailed What is the angle 180 degrees between the plane vector b and the vector a=(1,-2),|b|=3 roots 5, then b? Explain clearly, have problem solving process, detailed

A, b in the opposite direction, let b=λ(1,-2)=(λ,-2λ), and λ

It is proved that the non-zero vectors a and b satisfy |a|=|b|=|a-b|, then the included angle between a and a+b is 30°.

Let non-zero vector a, b be that angle between them be,
Then,|a-b|2=a2+b2-2|a||b|cosθ,
A|=|b|=|a-b|, replace |b| and |a-b| with |a|
Get cos θ=0.5θ=60°
The direction of a+b is in the same line as the bisector of angles a and b
The angle between a and a+b is 30°

Let non-zero vector a, b have an angle of θ,
Then,|a-b|2=a2+b2-2|a||b|cosθ,
A|=|b|=|a-b|, replace |b| and |a-b| with |a|
Get cos θ=0.5θ=60°
The direction of a+b is in the same line as the bisector of angles a and b
The angle between a and a+b is 30°

Let that non-zero vector a, b be at an angle of θ,
Then,|a-b|2=a2+b2-2|a||b|cosθ,
A|=|b|=|a-b|, replace |b| and |a-b| with |a|
Get cos θ=0.5θ=60°
The direction of a+b is in the same line as the bisector of angles a and b
The angle between a and a+b is 30°

1. Given two non-zero vectors a and b, define |a*b|=|a b|sinθ, where θ is the included angle between a and b, if a=(-3,4) b=(0,2) Then |a*b|=_______ 2. The image passing points (π/3,0) and (π/2,1) of the given function f (x)=asinx+bcosx, (1) Find the values of a and b,(2) when x is the sum value, f (x) gets the maximum

1A*b|=a b|sin a=(-3,4), b=(0,2) cosθ=a●b/(|a||b|)=8/(5*2)=4/5 sinθ=√(1-cos2θ)=3/5 a*b|=a b|sinθ=5*2*3/5=62(1) f (x)=asinx+bcosx image passing point (π/3,0)...

If not zero vector a, b satisfies |a+b|=|a-b|, then the angle between a and b is? If the nonzero vector a, b satisfies |a+b|=|a-b|, then the angle between a and b is?

90 Degrees. Only then |a+b| equals |a-b|