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A (2,1,-3) B (1,-2,4) is known as the unit vector in the same direction as vector AB
Analysis: If the vector AB=(1,-2,4)-(2,1,-3)=(-1,-3,7), then the module |AB|=root number (1+9+49)=root number 59, the unit vector which is collinear with the vector AB is the vector a, then: vector a=vector AB/|AB|=(-(root number 59)/59,-3(root number 59)/59,7(root number 59)/59) or vector a=-vector AB/|...
Given vector a=(1,-1), b=(2,4), find the unit vector e perpendicular to 2a+b
Vector a=(1,-1), b=(2,4)
Then 2a+b=(2,-2)+(2,4)=(4,2)
Let e=(x, y) be the unit vector perpendicular to 2a+b
Then {4x+2y=0
{X^2+y^2=1
5X^2=1, x^2=1/5, y^2=4/5
X=-√5/5, y=2√5/5
Or x=√5/5, y=-2√5/5
E=(-√5/5,2√/5) or e=(√5/5,-2√5/5)
Given vector a=(1,0) b=(1,1), then: find the coordinates of the unit vector in the same direction as 2a+b; What does the unit vector in the same direction mean, and how does the answer come about Given the vector a=(1,0) b=(1,1), then: find the coordinates of the unit vector in the same direction as 2a+b; What does the unit vector in the same direction mean, and how is the answer sought
Parsing:
The unit vector in the same direction is the vector with the same direction as vector 2a+b and the module length of 1
It means:
Because a =(1,0) b =(1,1)
Then 2a+b=(3,1)
By 1 x: y=3:1
2 X2+ y2=1
Solution x=3√10/10 y=√10/10
Therefore, the coordinate of the unit vector in the same direction of 2a+b is (3√10/10,√10/10)
If you understand and solve your problem,
Given that the vectors a.b are all unit vectors, and ab=1/2, the value of |2a-b| is?
Solution
A.b is the unit vector
/A/=1,/b/=1
Ab=1/2
/2A-b/
=√(2A-b)2
=√(4A2-4ab+b2)
=√4-4×1/2+1
=√5-2
=√3
If A =(2,3), B=(-4,7), then A In The projection in direction b is () A. 3 B. 13 5 C. 65 5 D. 65
Parsing:
A In
The projection in direction b is a•b
|B |=2×(−4)+3×7
(−4)2+72=13
65=
65
5.
Therefore, C
If a vector start point A (-2,4), end point B (2,1) find the unit vector coordinate parallel to a vector Vector a=(4,-3),|a|=√4^2+(-3)^2=5a0=±a/|a|=(0.8,-0.6) or (-0.8,0.6), why? If a vector start point A (-2,4) and end point B (2,1) find the unit vector coordinate parallel to a vector Vector a=(4,-3),|a|=√4^2+(-3)^2=5a0=±a/|a|=(0.8,-0.6) or (-0.8,0.6), why?
The unit vector e=a/|a|,(both e and a are vectors)
Vector AB=(4,-3)
Its modulus |AB |=5
So its unit vector e=(4/5,-3/5)
The unit vector e=a/|a|,(e and a are both vectors)
Vector AB=(4,-3)
Its modulus |AB |=5
So its unit vector e=(4/5,-3/5)
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