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Given that a and b are nonzero vectors, let θ be the angle between a and b, and ask if there is θ, so that |a+b|=3|a-b| under the root sign Find θ Given that a and b are nonzero vectors, let θ be the included angle between a and b, and ask if θ exists, so that |a+b|=3|a-b| under the root sign Find θ
|A+b|2=3|a-b|2==>2a2-8a*b+2b2=0==>|a|2-4|a||b|cos b|2=0
Cosθ=(|a|2 b|2)/4|a||b|
Cosθ has a minimum value of 1/2 when |a|=|b|
1/2≤Cosθ0o
Is the zero vector collinear with the zero vector
Zero vector and any vector parallel or collinear zero vector and zero vector can be said to be collinear or parallel but can also be said to be non-collinear non-parallel discussion of its no point
Known vector A =(1,2), vector B =(x,−2), and A⊥( A− B), then the real number x equals () A.-4 B.4 C.0 D.9
∵
A
A-
B)
A...
A-
B)=0,
∴
A...
A-
A...
B=0,
1+2×2-(1×X-2×2)0,
X=9.
Therefore, he chose D.
∵
A⊥(
A-
B)
A•(
A-
B)=0,
∴
A•
A-
A•
B =0,
1+2×2-(1×X-2×2)0,
X =9.
Therefore, D.
Given Point A (-1,5) and Vector A =(2,3) if AB =3 A, the coordinates of point B are () A.(7,4) B.(7,14) C.(5,4) D.(5,14)
Let B (x, y) be by
AB =3
A =(6,9),
Guyou
X+1=6
Y−5=9, solved
X =5
Y =14,
Therefore, D.
Given the vector AB=a+5b; BC=-2a+8b CD=3(a-b), which three points are collinear? Given the vector AB=a+5b; BC=-2a+8bCD=3(a-b), which three points are collinear?
OB-OA=AB=a+5b (1)
OC-OB=BC=-2a+8b (2)
OD-OC = CD =3(a-b)(3)
(2)+(3)
OD-OB=a+5b=AB
=> BD = AB
=> A,B,D 3 point collinear
Given vector set p={ vector a|vector a=(-1,1)+m (1,2) m∈R} Q={ vector b|vector b=(1,2)+n (2,3), n∈R} then P∩Q equals?
The answer is wrong. It is a multiple-choice question. The correct answer is (-13,-23). Take a look again and ask for a detailed explanation
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