Is a linear algebra problem," a set of nonzero n-dimensional vectors, if they are orthogonal to each other, then they are called orthogonal vector sets "orthogonal to any two vectors? Linear algebra problem," a set of nonzero n-dimensional vectors, if they are orthogonal to each other, it is called orthogonal vector set "is any two vectors orthogonal? Linear algebra problem," a set of nonzero n-dimensional vectors, if they are orthogonal to each other, then it is called orthogonal vector set "Is any two vectors orthogonal?

Is a linear algebra problem," a set of nonzero n-dimensional vectors, if they are orthogonal to each other, then they are called orthogonal vector sets "orthogonal to any two vectors? Linear algebra problem," a set of nonzero n-dimensional vectors, if they are orthogonal to each other, it is called orthogonal vector set "is any two vectors orthogonal? Linear algebra problem," a set of nonzero n-dimensional vectors, if they are orthogonal to each other, then it is called orthogonal vector set "Is any two vectors orthogonal?

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What is the specific meaning of "canonical orthogonality" of vector in linear algebra, why is canonical orthogonality carried out, and what is its use?

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Given vector a=(2,1), a*b=10,|a+b|=5 times root number 2,|b|=?

|A+b|=5 times the root number 2, then (|a+b|)2=(a+b)2=a2+2ab+b2=a2+2ab+|b|2=50
A =(2,1), a*b =10, then a2=5
So |b|=5

|A+b|=5 times the root number 2, then (|a+b|)2=(a+b)2=a2+2ab+b2=a2+2ab+|b|2=50
A =(2,1), a*b =10, then a2=5
So |b |=5

A Vector Judgment Let a, b, c be arbitrary nonzero plane vectors, not collinear with each other, then which of the following statements is true: 1.(A*b)*c-(c*a)*b=0 2.|A|-|b|<|a-b| 3.(B*c)*a-(c*a)*b is not perpendicular to c 4.(3A+2b)*(3a-2b)=9|a|2-4|b|2 Hope there's an analysis... Thank you.

1. Error. It is a common test point of vector quantity product. Both a.b and c.a are values with no direction, so the problem is that the difference between two non-collinear vectors is zero vector, which is impossible. Therefore, it can be known that the quantity product of vector does not satisfy the law of multiplication.2. Correct. Considering the relationship between three sides of triangle, the difference between two sides is less than the third side.3. Error.

A Vector Proof It is proved that AB times CD+BC times AC+CA times BD=0 for any quadrilateral ABCD It's BC, AD. Wrong. A Vector Proof It is proved that AB times CD+BC times AC+CA times BD=0 for any quadrilateral ABCD It's BC by AD. It's written wrong.

AC=AB+BC BD=BC+CD
Original formula =
AB times CD+BC times (AB+BC)-(AB+BC) times (BC+CD)
Open to simplify and remove the same item, the basic idea so that you write less than one item

A Proof of Vector The letters written below represent vectors. A+b+c=0 Verification AXb = bXc = cXa Note that cross multiplication is not a vector dot product, A Proof of Vector The letters written below represent vectors. A+b+c=0 Verification A Xb = bXc = cXa Note that cross multiplication is not a vector dot product,

For both sides of a+b+c=0, multiply a by left fork at the same time to obtain
AXb+aXc=0, shift term, get aXb=-aXc, so there is
AXb = cXa
The rest are the same

For a + b + c =0, multiply a by the left fork on both sides simultaneously.
AXb+aXc=0, shift term, get aXb=-aXc, so there is
AXb = cXa
The rest are the same