Find the coordinates of D which lies on the vector BC

In summary, the conversation involves finding the equation of a line from points B(-8,-3) to C(4,6), with point A assumed to be at the origin. The suggestion is made to start by drawing a diagram of the two vectors AC and AB, and using the "Attach files" link to upload it. The equation of the line can be found by finding the slope and using the point-slope form, and then the distance formula can be used to find point D, which is 5/11th of the way from B to C. The problem can also be solved using simple geometry and proportionality, but a diagram is needed for further assistance.
  • #1
MathMan2022
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Member warned that some effort must be shown in homework questions.
Homework Statement
Lets image we have two vectors AC = <4,6> and AB = <-8,-3> then find a point D which lies on the vector BC which satisfies that |BD|/|CD| = 5/6 ??
Relevant Equations
|BD| = 5/6 |CD|
Not sure on howto proceed here?
 
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  • #2
You know that you need to show your work before we can offer tutorial help.

Perhaps start by drawing a diagram of those two vectors to see if it gives you some ideas? You can use the "Attach files" link below the Edit window to upload a PDF or JPEG of your sketch...
 
  • #3
That I can figure out is that if I write <DB>=5/6<DC> then
<OD>-<OB>=5/6*(<OD>-<OC>)

But don't know howto proceed from there?
 
  • #4
MathMan2022 said:
But don't know howto proceed from there?
Find the equation of the line from B(-8, -3) to C(4, 6). I am assuming that point A is at the origin. You can do this by finding the slope of the line, and then the point-slope form of the equation of a line.
Once you have the equation of the line, use the distance formula to find point D. It would be at a the point that is 5/11th of the way from B to C.
 
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  • #5
MathMan2022 said:
Homework Statement:: Lets image we have two vectors AC = <4,6> and AB = <-8,-3> then find a point D which lies on the vector BC which satisfies that |BD|/|CD| = 5/6 ??
Relevant Equations:: |BD| = 5/6 |CD|

Not sure on howto proceed here?
Although it may not the required/intended method, note that the problem can easily be done with only simple geometry and proportionality.

But you haven't yet posted a diagram so I can't help more.
 
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1. What is the definition of a vector?

A vector is a mathematical object that has both magnitude (size) and direction. It is typically represented by an arrow, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction.

2. How do you find the coordinates of a point on a vector?

To find the coordinates of a point on a vector, you need to know the starting point (usually the origin) and the direction and magnitude of the vector. From there, you can use the coordinates of the starting point and the direction and magnitude of the vector to find the coordinates of the point on the vector.

3. What is the difference between a vector and a point?

A vector is a mathematical object that has both magnitude and direction, while a point is a specific location in space with no magnitude or direction. Vectors are used to represent movement or displacement, while points are used to represent specific locations.

4. How do you represent a vector on a coordinate plane?

A vector can be represented on a coordinate plane by using its starting point (usually the origin) and its direction and magnitude. The direction and magnitude can be represented by an arrow, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction.

5. How can you use vectors to solve real-world problems?

Vectors can be used to solve real-world problems by representing physical quantities such as velocity, acceleration, and force. They can also be used in navigation and mapping, as well as in computer graphics and animation. By understanding how to find the coordinates of points on vectors, you can use vectors to solve various mathematical and scientific problems.

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