- #1
Buzzlastyear
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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!