I need help with this problem!

Question

Find the linear equation of the plane through the point (1,2,3) and contain the line represented by the vector equation r(t)= <3t, 5-4t, 1-8t)

My answer was: 16x+14y+5z=59, but it is wrong. I need help showing me where I am wrong, please

Answer 1

r(t) = t<3, -4, -8> + <0, 5, 1>

w = <3, -4, -8> is parallel to the plane and v = <0-1, 5-2, 1-3> = <-1, 3, -2> is also parallel to the plane.

v x w is perpendicular to the plane.

v x w = <32, 14, 5>

Let (x, y, z) be an arbitrary point on the plane. So, <x - 1, y - 2, z - 3> is parallel to the plane.

<32, 14, 5> • <x - 1, y - 2, z - 3> = 0

32(x - 1) + 14(y - 2) + 5(z - 3) = 0

32x + 14y + 5z = 75