Scalar Equation of Plane Determining the value of k

[Buzzlastyear]

Homework Statement

Determine the value of k so that the line with parametric equations x = 2 + 3t, y = -2 + 5t, z = k is parallel to the plane with equation 4x + 3y – 3z -12 = 0.

Homework Equations

The Attempt at a Solution

let k=a + bt

x=2+3t
y=-2+5t
z=a+bt

direction vector= (3,5,b)

The normal to the equation 4x + 3y – 3z -12 = 0 is n=(4,3,-3)

Dot product of the direction vector and normal: (4,3,-3).(3,5,6)=0
12+15-3b=0
b=9
therefore z=a+9t

So:

x=2+3t
y=-2+5t
z=a+9t

not sure where to go from here

Thanks for any help!

 

[hamsterman]

The line you got is parallel to the plane for any value of a, maybe except the one where this line is on the plane (that seems to be when a=10/3). There is nothing wrong here.