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Given non-zero vectors a, b and a perpendicular to b, verify that (absolute value of vector a + absolute value of vector b)/(absolute value of vector a + b) is less than or equal to root 2
Let the length of vector a be ab and the length of vector a+b be c
Multiply both sides by (the absolute value of vector a+b) and square them simultaneously
Becomes (absolute value of vector a + absolute value of vector b) less than or equal to 2 times the square of (absolute value of vector a + b
I.e.(a+b)^2
Let the length of vector a be the length of a b be the length of b vector a+b be the length of c
Multiply both sides by (the absolute value of vector a+b) and square them simultaneously
Becomes (absolute value of vector a + absolute value of vector b) less than or equal to 2 times the square of (absolute value of vector a + b
I.e.(a+b)^2
If vectors a, b are not collinear, then the absolute value of their sum is greater than the absolute value of the difference if and only if?
Absolute value of sum is greater than absolute value of difference
Then │a+b│>│a-b│
Squared to a^2+b^2+2ab > a^2+b^2-2ab
Get ab >0
But ab is not collinear
So an angle of ab is an acute angle
Therefore, vectors a and b are not collinear, and the absolute value of their sum is greater than the absolute value of the difference if included angle of ab is an acute angle.
Absolute value of sum is greater than absolute value of difference
Then │a+b│>│a-b│
Squared to a^2+b^2+2ab > a^2+b^2-2ab
Get ab >0
But ab is not a common line
So an angle of ab is an acute angle
Therefore, vectors a and b are not collinear, and the absolute value of their sum is greater than the absolute value of the difference if included angle of ab is an acute angle.
Absolute value of sum is greater than absolute value of difference
Then │a+b│>│a-b│
Squared to a^2+b^2+2ab > a^2+b^2-2ab
Get ab >0
But ab is not collinear
So an angle of ab is an acute angle
Therefore, vectors a and b are not collinear, and the absolute value of their sum is greater than the absolute value of difference if the included angle of ab is acute.
How to find the absolute value of vector a
That's the film of vector a. There's a formula for finding the film in the book.
| A |=√(x2+y2+z2)
That's the film of vector a. There's a formula for finding a film in the book.
| A |=√(x2+y2+z2)
That's the film of vector a. There's a formula for the film in the book.
| A |=√(x2+y2+z2)
On the two non-zero vectors of a, b, the following conditions are given: where a = b is a necessary and insufficient condition 1|A|=|b|and a is parallel to b;2a^2=b^2;3a points multiplied by b=b square
1|A|=|b|, and a//b, i.e., a=b or a=-b, i.e., this conclusion can not be deduced a=b, but a=b can be deduced, i.e., necessary is not sufficient 2|a|^2=|b|^2, i.e.,|a||=|b|, i.e., this conclusion can not be deduced a=b, but a=b can be deduced, i.e., necessary is not sufficient 3a·b=|a||b|** cos=|b|^2, i.e., cos=|b||/|a| when:|a|
If AB is a nonzero vector, then |A+B|=|A-B| is valid if and only if A//B A and B have a common starting point | A |=| B | A⊥B
|A+B|=|A-B| A+B|2=A2+2AB+B2=|A-B|2=A22AB+B2 AB=0 A⊥B
Select 4 A⊥B
Know the coordinates of two vectors and how to multiply them Or modular multiplication. Isn't it the same with modular multiplication?
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