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Vectors: Vector Line to Cartesian form
The cartesian equation of the line with vector equation
(
x
y
)
 =
(
–8
4
)
 + lambda
(
4
–3
)
is y + x =

tickcross


Worked Solution:

From the vector equation's components we have:
x = –8 + 4 lambda
y = 4 – 3 lambda
Rearranging, we have two equations for lambda:
lambda =
x + 8
---
4
 =
y – 4
---
–3
Multiplying by –12:
–3 x – 24 = 4 y – 16
<=> –8 = 4 y + 3 x is the cartesian equation of the line.
This is not the only correct answer because any multiple of this equation gives the same line.

© MEI Produced by Dr Ron Knott, 19 May 2004
tom . button [AT] mei . org . uk 		Test reference: VectorsLineE.html?ref=20020