Find a point on the curve Γ: x = t, y = T ^ 2, z = T ^ 3 so that the tangent of the point is parallel to the plane π: x + 2Y + Z = 4

Find a point on the curve Γ: x = t, y = T ^ 2, z = T ^ 3 so that the tangent of the point is parallel to the plane π: x + 2Y + Z = 4

Tangent slope of curve X = t, y = T ^ 2, z = T ^ 3
x=1,y = 2t,z=3t^2
The tangent is parallel to the plane x + 2Y + Z = 4, and the product of the tangent slope and the normal vector of the plane is 0
1*1+2t*2+3t^2*1 = 0
T = - 1 or - 1 / 3, which is substituted into the linear equation
X = - 1, y = 1, z = - 1, or x = - 1 / 3, y = 1 / 9, z = - 1 / 27

Elden Ring Premiere

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