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The Most Basic Conceptual Knowledge of [Senior Mathematics] Vector 》》》 Which of the following equations is wrong? (1)0-A=-a (2)-(-A)=a (3) A+(-a)=0 (4) A +0= a (5) A-b=a+(-b) (6) A+(-a)=0 Which is wrong and why? "A,0 are all vectors 》》》》》》》》》 The Most Basic Conceptual Knowledge of [Senior Mathematics] Vector 》》》 Which of the following equations is wrong? (1)0-A=-a (2)-(-A)=a (3) A+(-a)=0 (4) A+0= a (5) A-b=a+(-b) (6) A+(-a)=0 Which is wrong and why? "A,0 are all vectors 》》》》》》》》》
0
Let vector a and vector b be collinear vectors, with the module of vector a=3 and the module of vector b=5, then vector a is multiplied by vector b =-----------
Vector a and vector b are collinear vectors
Cos (a, b)=1
Cos (a, b)=ab/|a||b|=1
Ab=|a||b|=3*5=15
Given vector |a|=2. Vector b=(1.-1). And vector a vertical vector b, find the coordinates of vector a
0
[Senior One Mathematics] Given vector ab satisfies |a|=12|b|=15|a+b|=25 find |a-b|
(A+b)^2=625 from |a+b|=25,
I.e. a^2+2a*b+b^2=625,
So 144+2a*b+225=625,
Solution 2a*b =256,
So, from (a-b)^2=a^2-2a*b+b^2=144-256+225=113,|a-b|=√113.
(A+b)^2=625 from |a+b|=25,
I.e. a^2+2a*b+b^2=625,
So 144+2a*b+225=625,
Solution 2a*b=256,
So, from (a-b)^2=a^2-2a*b+b^2=144-256+225=113,|a-b|=√113.
The vector a =3, vector b =4, and the angle θ between vector a and vector b =150 degrees... 1. Given vector |a|=3, vector |b|=4, and the included angle θ between vector a and vector b=150°, find a*b,(a+b)^2,|a+b|(the letters in the problem represent vectors) 2, Known |a|=2,|b|=5, a*b=-3, find |a+b|,|a-b|(letters in the problem represent vectors)
1
Cos (a, b)= cos150°=- cos30°= ab/|a b|
Ab=-√3/2*3*4=-6√3
(A+b)^2=a^2+2ab+b^2=3^2+2*(-6√3)+4^2=25-12√3
|A+b|=√(a+b)^2=√(25-12√3)
2
|A+b|=√(a+b)^2=√(a^2+2ab+b^2)=√(2^2+2*(-3)+5^2)=√23
|A-b|=√(a-b)^2=√(a^2-2ab+b^2)=√(2^2-2*(-3)+5^2)=√35
Solving the Problem of "the Quantity Product of Plane Vector" in Senior One Mathematics The following relations about the product of the number of vectors:1, vector of 0* vector of 0=0 2.| Vector of a * vector of b | vector of a * b | vector of less than or equal to a 3, vector of a ^2=| vector of a |^2 4. Vector a * vector b /| vector a |^2= vector b / vector a 5,(vector a * vector b)^2= vector a ^2* vector b ^2 6.(Vector of a - vector of b)^2= vector of a ^2-2a * vector of b + vector of b ^2, where are the correct ones? Why?
1. Right
2. Error. When the angle between the vector of a and the vector of b is greater than 90, the vector | of the vector of a*b is greater than or equal to the vector of a*b.
3. Right
4. Wrong. Cosx is the angle between vectors.
And cosx is the angle between vectors.
6. Yes.
The commutative law of a vector doesn't hold.
1. Right
2. Error. When the angle between the vector of a and the vector of b is greater than 90, the vector | of the vector of a*b is greater than or equal to the vector of a*b.
3. Right
And cosx is the angle between vectors.
And cosx is the angle between vectors.
6. Yes.
The commutative law of a vector doesn't hold.
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