Vector lines, ratio of vector lines

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SUMMARY

The discussion focuses on the calculation of vector lines and their ratios, specifically using the equation r = a + λb. The user initially calculated the vector AB as (2, 2, -2) and derived the line equation (1, 0, -1) + λ(2, 2, -2). The midpoint OM was correctly identified as (2, 1, -2) with λ set to 0.5. However, the user incorrectly set λ for the vector AC as 1/3 instead of the correct value of 2/3, which accurately represents the position of point N, located 2/3 of the way from A to C.

PREREQUISITES
  • Understanding of vector equations and their components
  • Familiarity with the concept of parameterization in vector lines
  • Knowledge of midpoint calculations in three-dimensional space
  • Ability to manipulate and solve equations involving λ (lambda)
NEXT STEPS
  • Study vector parameterization techniques in depth
  • Learn about calculating midpoints in three-dimensional geometry
  • Explore the application of ratios in vector lines
  • Practice solving vector equations with varying values of λ
USEFUL FOR

Students studying mathematics at the A Level, particularly those focusing on vector geometry, as well as educators seeking to clarify concepts related to vector lines and their ratios.

thoradicus
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http://www.xtremepapers.com/papers/CIE/Cambridge%20International%20A%20and%20AS%20Level/Mathematics%20%289709%29/9709_w09_qp_31.pdf

Homework Statement


6i


Homework Equations


r=a+λb


The Attempt at a Solution


first i find AB which is (2,2,-2)
the equation if line is then (1,0,-1)+λ(2,2,-2)
i made it so that λ is 0.5, which then OM is (2,1,-2), as its the mid point.

i found AC to be (3,-3,3)

the equation of AC is (1,0,-1)+λ(3,-3,3)
which then i made lambda to be 1/3...but is this the right working? i did that and i can't get the awnser.
 
Physics news on Phys.org
N is 2/3 of the way from A to C so is closer to C than A. Take \lambda= 2/3, not 1/3.
 
gah, didnt notice that. I am such an idiot >< thanks a lot.
 

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