To find the midpoint of a line AB,with the given points A and B

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In summary: Now, can you find the unit vector in the direction from the origin to that point?In summary, to find the unit vector extending from the origin towards the midpoint of line AB, first calculate the midpoint using the formula for finding the midpoint between two points. The midpoint for points A=(4,3,2) and B=(-2,0,5) is (1,1.5,3.5). Then, use this midpoint to find the unit vector in the direction from the origin to the midpoint by dividing the direction vector (-3i-1.5j+1.5k) by its magnitude, which is √(9+2.25+2.25). This will give the desired unit vector
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Abel I Daniel
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Homework Statement


*)Given two points A=(4,3,2) and B=(-2,0,5).Find the unit vector extending from origin toward the midpoint of line AB


Homework Equations





The Attempt at a Solution



Direction vector to AB=(-6,-3,3) and hence direction vector to its midpoint is (-3,-1.5,1.5)
So unit vector in the direction of (-3,-1.5,1.5) is (-3i-1.5j+1.5k)/√(9+2.25+2.25).

Is this the way to do it??
 
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  • #2
I doubt that you have begun this correctly, but my maths is very rusty.

Perhaps you should take another look at it by first calculating the midpoint of line AB.
 
  • #3
Abel I Daniel said:

Homework Statement


*)Given two points A=(4,3,2) and B=(-2,0,5).Find the unit vector extending from origin toward the midpoint of line AB


Homework Equations





The Attempt at a Solution



Direction vector to AB=(-6,-3,3) and hence direction vector to its midpoint is (-3,-1.5,1.5)
So unit vector in the direction of (-3,-1.5,1.5) is (-3i-1.5j+1.5k)/√(9+2.25+2.25).

Is this the way to do it??

No. Look up the formula for the mid-point between two points.
 
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  • #4
oh,i got wrong with the midpoint formula..so now the midpoint is (1,1.5,3.5).is it correct??
 
  • #5
Abel I Daniel said:
oh,i got wrong with the midpoint formula..so now the midpoint is (1,1.5,3.5).is it correct??
That is the midpoint, yes.
 
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1. What is the formula for finding the midpoint of a line?

The formula for finding the midpoint of a line is (x1 + x2)/2, (y1 + y2)/2.

2. How do I find the coordinates of a midpoint?

To find the coordinates of the midpoint of a line AB, you will need the coordinates of points A and B. Then, plug these values into the midpoint formula (x1 + x2)/2, (y1 + y2)/2 to calculate the midpoint's coordinates.

3. Can I use the distance formula to find the midpoint of a line?

No, the distance formula is used to calculate the length of a line, not the midpoint. The midpoint formula is specifically designed to find the coordinates of the midpoint.

4. Is the midpoint of a line always halfway between the two points?

Yes, by definition, the midpoint of a line is exactly halfway between the two points. This means that the distance from one point to the midpoint is equal to the distance from the midpoint to the other point.

5. How does finding the midpoint of a line help in geometry?

Finding the midpoint of a line is helpful in geometry because it allows us to divide a line into two equal segments. This can be useful in various geometric constructions and calculations, such as finding the center of a circle or bisecting an angle.

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