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**icelated** I have an odd problem in the book where i have no solution to and i am not sure if i am doing it correctly.

Let L be the line given by $\displaystyle x = 3-t, y=2+t, z= -4 +2t$

L intersects the plane $\displaystyle 3x-2y+z=1$ at the point $\displaystyle P=(3, 2, -4)$

Find parametric equations for the line through P which lies in the plane and is perpendicular to L

**Attempt:**

Direction Vector v = $\displaystyle <-1,1,2>$

Normal Vector n = $\displaystyle <3, -2, 1>$

$\displaystyle v \times n = <5, 7, -1>$

$\displaystyle X = P + vt$

Point: $\displaystyle P=(3, 2, -4)$

v = $\displaystyle <-1,1,2>$

putting it together

$\displaystyle (3, 2, -4) + <-1,1,2>t$

Parametric equation: $\displaystyle x = 3-t, y = 2+t , z = -4 +2t$

Somehow, i dont think this is correct?