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## Homework Statement

The position vectors of two points a and b on a line are < 2,1,7> and < 1,4,-1>

Find the parametric vector equation for any point on the line.

Find the linear Cartesian equation of the line using x, y, z as coordinates.

## Homework Equations

For the parametric eq.

x = a + λu where u is a unit vector

## The Attempt at a Solution

b -a = < -1, 3, -8 > , call it u

Norm of b -a = √(-1)^2 + (3)^2 + -(-8)^2

unit vector

**u**= <-1/√74, 3/ √74 , -8 /√74>

x = < 2, 1, 7 > + λ<-1/√74, 3/ √74 , -8 /√74>

For the Cartesian equation I have.

x = 2 + λ(-1/√74)

y = 1 + λ(3/ √74)

z = 7 + λ(-8 /√74)

How is she looking?

I have a question if it says linear Cartesian equation does that mean I have to eliminate lambda and write it all together or it is fine to leave as I have?

Thanks