Knowing a b 2, 8 , a b 8, 16 , then the cosine value of the angle between a and b is

The main part of whzany is correct, but the clear statement should be:

is composed of equations x1+x2=2,x1-x2=-8;y1+y2=-8, y1-y2=16 solve a=(-3,4),b=(5,-12). Find the inner product of a and b: ==(-3) 5+4 (12) = -63, and find the modulus of a and b

a|=5，|b|=13。

Therefore: cos (a,b)=-63 (5 13)=-63 65.

First, we get a=(-3,4), b=(5,-12), and then point a multiplies b by |a*b|=-63/65

a+b=(2,-8),a-b=(-8,16)plus 2a=(-6,8) a=(-3,4)minus 2b=(10,-24) b=(5,-12)a|=5,|b|=13

The cosine value of the grinding and rolling at the angle between cos=a and b is -63 and 65

Let a=(m,n),b=(x,y).

It can be obtained from a+b=(2,-8),a-b=(panicle nucleus-8,6).

m+x=2n+y=-8

m-x=-8

n-y=6 solution hall lack m=-3,x=5,n=-1,y=-7a=(-3,-1),b=(5,-7).

cos(a,b)=(15+7) (10 74)-4 185

Summary. The method used is as follows: plane vector proof method a+b=c, (parallelogram rule: the diagonal line between two adjacent sides represents the size of the two adjacent edges) c·c=(a+b)· (a+b)。

c2=a·a+2a·b+b·b∴c2=a2+b2+2|a||b|cos( - the above bold characters represent vectors) and cos( -cosc, c2=a2+b2-2|a||b|cosθ。(Note: the trigonometric formula is used here) and then disassemble it to get c2=a2+b2-2abcosc, that is, cosc=.

The same can be said for others, and the following cosc=(c2-b2-a2) (2ab) is to move the cosc to the left.

13.Knowing a=(2,-1),b-(0,1), then the cosine value of the angle between 2a-b and b is .

Hello, 13If it is known that the cosine value of the angle between 2a-b and b is known, then the solution of the cosine value of the angle between 2a-b and b is as follows: 13Knowing that a=(2,-1),b-(0,1), then the cosine value of the angle between 2a-b and b is -3 5 oh pro.

Related information: Cosine (cosine good first function), a type of trigonometric function. In RT abc (right triangle), c = 90° (as shown in the overview figure), the cosine of the friendly rock number of a is its adjacent edge than the hypotenuse of the triangle jujube brigade, i.e., cosa=b c, which can also be written as cosa=ac ab.

Cosine function: f(x)=cosx(x r).

The method used is as follows, You Bi is suspicious of the plane vector method a+b=c, (parallelogram rule: the diagonal line between two adjacent edges represents the size of the two adjacent edges) c·c=(a+b)· (a+b)。 ∴c2=a·a+2a·b+b·b∴c2=a2+b2+2|a||b|cos( - the above bold characters represent vectors) and cos( -cosc, c2=a2+b2-2|a||b|cosθ。

Pay attention to the hand of God: the trigonometric formula is used here) and then disassemble the wisdom match, and get c2=a2+b2-2abcosc, that is, cosc=. The same can be said for others, and the following cosc=(c2-b2-a2) (2ab) is to move the cosc to the left.

The specific process is as follows.

14.The known function f(x)- <2(a", r 2 is monotonically increasing on r, then the range of a is .

14.The known function f(x)- <2(a", r 2 is monotonically increasing on r, then the range of a is .

A can range from -3 to 2 oh pro.

21.(12 points) Let the positive term series satisfy the hermit grandchild a:=1, and nan-(n+da!).

n+n(nen')。1) Proof : The number of barricades (No. 2) is set to 6

It is the difference series of the stove balance chain and the number series (a) formula.

From the meaning of the title, we can know that an=n

The cross product of the two vectors can be calculated by the following formula:

a × b = a| |b|sin n where, |a|and |b|denotes the length of the lead with a and b, denotes the angle between a and b, and n denotes the unit vector perpendicular to the plane where a and b are located.

Substituting the coordinates of a and b into this formula, we get:

a × b = 6, -1, -7)

Secondly, the dot product of two vectors can be calculated by the following formula:

a · b = a| |b| cosθ

Substituting the coordinates of a and b into this formula, we get:

a · b = 2 1 + 3 (-1) +1 2 = 1 Finally, the angle cosine between two vectors can be calculated by the following formula:

cosθ =a · b / a| |b|Substituting the coordinates of a and b into this formula, we get:

a| =2² +3² +1²) 14

b| =1² +1)² 2²) 6

cos =1 14 6) =6 14) =3 7 Therefore, the cross product of vectors a and b is (6, -1, -7), the dot product is 1, and the angular cosine is 3 7.

a+b=(2,-8),a-b=(-8,16)Add 2a=(-6,8) a=(-3,4)Subtract 2b=(10,-24) b=(5,-12)|a|=5,|b|=13

The cosine value of the angle between cos=a and b is -63 65

Let a=(m,n),b=(x,y).

m+x=2 can be obtained from a+b=(2,-8),a-b=(-8,6).

n+y=-8

m-x=-8

n-y=6 gives m=-3, x=5, n=-1, y=-7

a=(-3,-1),b=(5,-7)

cos(a,b)=(-15+7) at the power side of Jiajia Huang Fat wilting Bolian (10 74).

Vector, or you can't do it.

a+b) (2a-b), (a-2b) (2a+b), a+b) (2a-b)=0 and, (a-2b) (2a+b)=0, i.e., 2a +ab-b =0 and 2a -3ab-2b =0 are subtracted: 4ab=b

All of the above are vectors).

4|a||b|cos=|b||b|

Eliminate, move item: cos=|b|/4|a|

There should also be ||in the titlea|、|b|or can be found. Your questions are incomplete.

Solution: Square both sides of 丨a+b丨=2丨a-b丨 to get 丨a+b丨 =4丨a-b丨

Unpack a +2 a b + b = 4 a -8ab + 4 b

10ab = 3 a + 3 b

then ab = 15 10 = 3 2

cosθ=ab/｜a｜｜b｜=3/4

From the question丨a+b丨 2=(2丨a-b丨) 2

a^2+2ab+b^2=4a^2-8ab+4b^2ab=5/2

cos angle = (ab) (丨a丨丨b丨) = 5 4