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Relationship between zero vector and non-zero vector, parallel or vertical?
All co-directional vectors are parallel!
Vector a, b, a+b is a nonzero vector and |vector a+b|=|vector a-b|, then {which of vector a=b, a perpendicular b,|a|=|b|}
There are two ideas for this question. I'll give them to you.
The first is the algebraic operation.
|Vector a+b|=|Vector a-b|This condition is equivalent to |vector a+b|^2=|vector a-b|^2 squared, expand this expression
A^2+b^2+2a·b=a^2+b^2-2a·b (Vector symbol omitted below)
Thus 4a·b=0, a·b=0, of course a is perpendicular to b.
The second idea is to use geometry.
The vector a+b|=|the vector a-b| shows that a+b and a-b are of the same length. Draw a graph to show that if a and b are two parallelograms, a+b is a diagonal of the parallelogram from the angle between a and b, and a-b is another diagonal connecting the points between a and b. The vector a+b|=|the vector a-b| indicates that the two diagonals of the parallelogram are of the same length. According to the plane geometry of junior high school, the parallelogram must be rectangular, so that the two sides are vertical, i.e. a is perpendicular to b.
This is a basic concept problem, should learn to analyze.
If |vector a|=0, then vector a=0 is correct If | vector a|=0, then vector a=0 is correct
The vector should have length and direction,| the vector a|=0 only indicates the vector length, so wrong, the correct vector should be vector a=0(0 has →)
The vector should have length and direction,| the vector a|=0 only indicates the length of the vector, so wrong, the correct vector should be vector a=0(0 has →)
Vector should have length and direction,| vector a|=0 only indicates the length of vector, so wrong, the correct vector should be vector a=0(0 has →)
Known A =3 I+2 J- K, B= I- J+2 K, then 5 A and 3 B is equal to ___.
A =3
I+2
J-
K =(3,2,-1),5
A =(15,10,-5)
B=
I-
J+2
K =(1,-1,2),3
B =(3,-3,6)
5
A•3
B=15×3+10×(-3)+(-5)×6=-15
Therefore, the answer is:-15
0 Vector -a vector =-a vector 0 Vector -(-a vector)= a vector A vector +(-a vector)=0 vector Are the three equations right or wrong? [For reasons...] 0 Vector -a vector =-a vector 0 Vector -(-a vector)= a vector A vector +(-a vector)=0 vector Are the three equations right or wrong? [Reasons...]
0-A =-a pair
0-(-A)=0+a = a pair
A+(-a)= a - a =0 pair
Given that a and b are nonzero vectors, and (a+b)⊥(a-b),(a+2b)⊥(2a-b), the included angle between 3a+4b and 2a+b is obtained.
Set the included angle as a, cosa=(3a+4b).(2a+b)/|3a+4b|.|2a+b|
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