Given vector a=(-1, y) vector b=(1,-3) and satisfy (2a+b)⊥b 1. Find the coordinates of vector a 2. Find the angle between vectors a and b Vector a=(-1, y) vector b=(1,-3) and satisfies (2a+b)⊥b 1. Find the coordinates of vector a 2. Find the angle between vectors a and b

Given vector a=(-1, y) vector b=(1,-3) and satisfy (2a+b)⊥b 1. Find the coordinates of vector a 2. Find the angle between vectors a and b Vector a=(-1, y) vector b=(1,-3) and satisfies (2a+b)⊥b 1. Find the coordinates of vector a 2. Find the angle between vectors a and b

1,2A+b=(-1,2y-3)
(2A+b)⊥b
3=2Y-3
2Y =6
Y =3
A (-1,3)
2, CosA=(-1-9)/10=-1
A =180°

Given vector a, b satisfies |a|=3, and |a+b|=|a-b|=5, find |b|

|A+b|=|a-b|=5, the vector a is multiplied by the vector b=0
A^2+b^2=25
B^2=16
|B |=4

Given vector a, b satisfies the value of /a/=1./b/=2,/a-b/=2 and /a+b/? Don't accumulate quantity, do n' t learn! Given the vector a, b satisfies the value of /a/=1./b/=2,/a-b/=2/a+b/? Don't accumulate quantity, do n' t learn!

Draw a picture,
Using the sum of squares of diagonals in a parallelogram = sum of squares of four sides
∴| A+b|2 a-b|2=2|a|2+2|b|2
∴| A+b|2+4=2+8
∴| A+b|2=6
∴| A + b |=√6

Let vector group α1,α2,α3,α4 be linearly independent, and vector group β1=α1,β2=α1+α2,β3=α1+α2+α3,β4=α1+α2+α3+α4. It is proved that vector group β1,β2,β3,β4 are also linearly independent.

Inverse proof method. Let β1,β2,β3,β4 be linearly related, then there is a x1,x2,x3,x4, that is not completely 0, so that: x1 1+x2 2+x3 3 x4 4=0. Because:β1=α1,β2=α1 2,β3=α1 2 3,β4=α1 2 3 3 4, so:4*x1 1+3*x2 2*2*x3 3 x4 4=0.

Does the maximum linearly independent "group" necessarily require two linearly independent vectors? Can it be composed of a vector that satisfies the linear independent group condition? Can a vector also be called a group? Does the maximal linearly independent "group" necessarily require two linearly independent vectors? Can it be composed of a vector that satisfies the linear independent group condition? Can a vector also be called a group?

Sure!
Such as vector group (1,0,0),(2,0,0),(3,0,0),
(1,0,0) Is a maximal independent group of vector groups.

Sure!
Such as vector group (1,0,0),(2,0,0),(3,0,0),
(1,0,0) A maximal independent group of vector groups.

Let vector a=(2,1,2) b=(4,-1,0) c=b-λa, and a⊥c, then λ= Let vector a=(2,1,2) b=(4,-1,0) c=b-λa, and a⊥c, then λ=

Solution c=b-λa=(4,-1,0)-λ(4,-1,0)=(4-4λ,-1+λ,0)
From a⊥c,
I.e. a*c=2*(4-4λ)+1*(-1+λ)+0*0=0
I.e.8-8λ-1=0
I.e.7λ=7
I.e.λ=1