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What is the unit vector in the same direction as vector α=(—3,—4)? What is the unit vector in the same direction as vector α=(-3,-4)?
The unit vector is (3/5 under the root,4/5 under the root), and the same as its unit vector is (3/5 under the n-fold root,4/5 under the m-fold root)
The unit vector is (3/5 below the root,4/5 below the root), and the same as its unit vector is (3/5 below the n-fold root,4/5 below the m-fold root)
Let a, b, c be vector units and a-b=c, then the angle of vectors a, b
│A│=│b│=│c│
A-b=c
Therefore a*a-2ab+b*b=c*c
So 1-2*1*1 cosa+1=1
Get cosa=1/2
So the angle between a and b is π/6
│A│=│b│=│c│
A-b=c
Therefore a*a-2ab+b*b=c*c
So 1-2*1*1 cosa+1=1
Get cosa =1/2
So the angle between a and b is π/6
Is the coordinate of the unit vector c equal to the angle of vectors a (1,2), b (2,1)? The coordinates of the unit vector c equal to the included angle of the vectors a (1,2), b (2,1)?
C =(x, y)
Cos
2X+y=x+2y
│C│=1
X2+ y2=1
X =√2/2, y =√2/2
X=-√2/2, y=-√2/2
Let n and m be two unit vectors with an angle of 60°. Try to find the angle of vector a=2m+n and b=2n-m.
Given that m, n are two unit vectors, the absolute value M and the absolute value N are both equal to 1, because the angle is 60°
So vector M*N=absolute value M*absolute value N*COS60°=1/2
Vector a* Vector b=4mn-6m*m+2n*n-3mn=1/2-4=-7/2
The absolute value of vector a is root number (2m+n)*(2m+n)= root number 7
Similarly, absolute value of vector b is root number 7
So -7/2= Root 7* Root 7* COS Angle
COS angle =-1/2
So angle =120
Let n and m be two unit vectors with an angle of 60 degrees, and find the angle between vector a=2m+n and b=2n-3m
|Vector a|2=|2m+n|2=(2m+n)2=4m2+n2+4m.n=4+1+4*1*1*cos60°=7|vector a|=√7|vector b|2=|2n-3m|2=(2n-3m)2=4n2+9m2-12m.n=4+9-12*1*1*cos60°=7|vector b|=√7 and...
Given that vector mn is two unit vectors with an included angle of 60 degrees, the included angle between vector a=2m+n and vector b=-3m=2n is?
B=?
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