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surface in space parameterised by x(u, v):

x(t)= <2+t, -t, 1+3t

^{2}>

x(u,v)=(u

^{2}- v + u, u+5, v-2>

A) Show that the curve intersects the surface in exactly two points. Show that

x

_{i}= <4 - [tex]\frac{\sqrt{46}}{2}[/tex], -2 + [tex]\frac{\sqrt{46}}{2}[/tex], [tex]\frac{95}{2}[/tex] - 6[tex]\sqrt{46}[/tex]

is one of them

B) Find the Tangential equation [tex]\frac{dx}{dt}[/tex] at x

_{i}

C) find the normal vector

n=[tex]\frac{dx(u,v)}{du}[/tex] x [tex]\frac{dx(u,v)}{dv}[/tex]

at x

_{i}

D)If [tex]\phi[/tex] with 0 [tex]\leq[/tex] [tex]\phi[/tex] [tex]\leq[/tex] 90 denotes the angle between the normal vector and the tangential vector, calculate for the intersection point x

_{i}(3 signcant figures).

Ive got an idea what to do with A. Make each part of the matrix eaqual to each other and the solve. But to be honest i don't even know if that's right either.

Thanks for the help in advance.