Finding the Ratio of a Vector Division: Vector Equation Help

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In summary, the vector AM is described by the equation r = (0,0,6) + x(0,-4,-6). To find the coordinates of point N, we can use the formula (r-A)^2=2^2*(r-M)^2 and solve for x. Alternatively, we can see that x=0 gives point A and x=1 gives point M, so the x value that splits the vector 2:1 must be 2/3. However, the given answer is 9/13, which is different from 2/3.
  • #1
Firepanda
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http://img404.imageshack.us/img404/5186/vectornw4.jpg

'Write Down the vector AM and hence the coords of the point N which divides AM so that the ratio AN:NM = 2:1.'

I know that ON = OA + AN

And that the vecor equation is

r = (0,0,6) + x(0,-4,-6)

But the answer is 9/13 for x, which i don't understand. I thought it would be 2/3 or 2/3 of the length AM. I am really stuck.

Thanks
 
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  • #2
Just take (r-A)^2=2^2*(r-M)^2 and solve for x. Or just notice x=0 gives A and x=1 gives M so the x that splits it 2:1 must be 2/3.
 
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  • #3
so ur saying x = 2/3?

thats what i said, but the answer says its 9/13 which i don't understand.
 
  • #4
Firepanda said:
so ur saying x = 2/3?

thats what i said, but the answer says its 9/13 which i don't understand.

If I'm understanding the question, yes, I say x=2/3.
 

FAQ: Finding the Ratio of a Vector Division: Vector Equation Help

What is a vector equation problem?

A vector equation problem involves solving for unknown variables in a system of equations that represent vectors in space. These equations typically involve both magnitude and direction, and can be solved using algebraic techniques.

What types of problems can be solved using vector equations?

Vector equations are commonly used in physics, engineering, and other fields to solve problems involving forces, motion, and geometry. They can also be used to solve problems in linear algebra and other areas of mathematics.

How do you solve a vector equation problem?

To solve a vector equation problem, you first need to set up the equations using the given information. Then, you can use algebraic techniques such as substitution, elimination, or matrix operations to solve for the unknown variables.

What are some common mistakes when solving vector equation problems?

Some common mistakes when solving vector equation problems include incorrect calculation of magnitude or direction, using the wrong units, and forgetting to include all relevant variables in the equations. It is important to carefully check all calculations and make sure all variables are included.

Are there any tips for solving vector equation problems?

Yes, some tips for solving vector equation problems include drawing diagrams to visualize the problem, breaking down complex equations into simpler components, and checking your answers to ensure they make sense in the context of the problem. It can also be helpful to practice solving various types of vector equation problems to improve your skills.

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