Given that M={ a|a=(2 1,-2-2), R}, N={ b|b=(3 2,6 1), R}, is a set of vectors, then M∩N= Options have four A {c|c (-2,1)} B {c|c (2,1)} C {c|c (-2,1)} D {c|c (2,1)}

Given that M={ a|a=(2 1,-2-2), R}, N={ b|b=(3 2,6 1), R}, is a set of vectors, then M∩N= Options have four A {c|c (-2,1)} B {c|c (2,1)} C {c|c (-2,1)} D {c|c (2,1)}

Let a=(2m+1,-2-2m), b=(3n-2,6n+1)
Then:
2M+1=3n-2
-2-2M=6n+1
Solution: m=-3/2, n=0, then:
M∩N ={(-2,1)}

If vector m =4, vector n =6, the angle between vector m and vector n is 135 degrees, then vector m * vector n is equal to?

Negative 12 times root sign 2

Vector a=(m, n), b=(p, q), and m+n=5, p+q=3, then what is the minimum value of |a+b|? Please write down the steps

Write important inequalities first:
If a+b= constant, a2+b2 has a minimum value (a+b)2/2, i.e. a2+b2>=(a+b)2/2
This inequality is the basic inequality, can be directly used in the exercise, it is not difficult to prove ~
A+b=(m+p, n+q)
|A+b|2
=(M+p)2+(n+q)2
=(M+p)2+((5-m)+(3-p))2
=(M+p)2+(8-(m+p))2
Conditions for Using Inequalities
>=(( M+n)+(8-(m+p)))2/2
=8²/2
=32
|A+b|>=4(root 2)
The minimum value for |a+b| is 4(root 2)

Given vector a=(m, n), vector b=(p, q), and m+n=5, p+q=3, then the minimum value of |a+b|

First, write the important inequality: if a+b = constant value, then a2+b2 has the minimum value (a+b)2/2, i.e. a2+b2>=(a+b)2/2 This inequality is the basic inequality, which can be directly used in the exercise, and it is not difficult to prove ~a+b=(m+p, n+q)|a+b|2=(m+p)2+(n+q)...

First, write the important inequality: if a+b = constant value, then a2+b2 has the minimum value (a+b)2/2, i.e. a2+b2>=(a+b)2/2. This inequality is the basic inequality, which can be directly used in the exercise. It is not difficult to prove that ~a+b=(m+p, n+q)|a+b|2=(m+p)2+(n+q)...

In △ABC, point P is on BC, and vector BP=2 vector PC, point Q is the midpoint of AC, if vector PA=(4,3), vector PQ=(1,5), vector BC=

BP=2PC
Q is the midpoint of AC
=> AQ = QC =(1/2) AC
PA=(4,3), PQ=(1,5)
BC = BP+PC
=3PC
=3(PA + AC)
=3(PA +2AQ)
=3(PA +2(-PA + PQ))
= 3((4,3) + 2(-3,2))
= 3((-2,7))
=(-6,21)

It is known that in △ABC,∠A=90°, BC=1, the length of the moving line segment PQ passing through point A is 2, and A is exactly the midpoint of the line segment PQ, when the line segment PQ rotates arbitrarily around point A, BP• Minimum value of CQ equals ______. It is known that in △ABC,∠A=90°, BC=1, the length of the moving line segment PQ passing through point A is 2, and A is exactly the midpoint of the line segment PQ, when the line segment PQ rotates arbitrarily around point A, BP• The minimum value of CQ is equal to ______.

As shown in the figure,
Let B (cosθ,0), C (0, sinθ), P (cosα, sinα),
Q (-cosα,-sinα).
∴

BP•

CQ=(cosα-cosθ, sinα)•(-cosα,-sinα-sinθ)
=-Cos2 coθscosα-sin2α-sinαsinθ
= Cos ()-1≥-2.
Therefore, the answer is:-2.