Find the coordinates of D which lies on the vector BC

[MathMan2022]

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?

 

[berkeman]

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...

 

[MathMan2022]

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?

 

[Mark44]

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.

 

[Steve4Physics]

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.