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Amanda [17]
3 years ago
5

Suppose you need to know an equation of the tangent plane to a surface S at the point P(4, 1, 4). You don't have an equation for

S but you know that the curves r1(t) = 4 + 3t, 1 − t2, 4 − 5t + t2 r2(u) = 3 + u2, 2u3 − 1, 2u + 2 both lie on S. Find an equation of the tangent plane at P.
Mathematics
1 answer:
Alex777 [14]3 years ago
5 0

Answer:

15x-8y+9z=88

Step-by-step explanation:

We are given that

Equation of curves

r_1(t)=

r_2(u)=

Both curves lie on S.

We have to find the equation of tangent plane at P(4,1,4).

r'_1(t)=,r'_2(u)=

r_1(0)=, r_2(1)=

Hence, t=0 and u then it satisfied the given point.

Substitute the values in the derivatives

r'_1(0)=,r'_2(1)=

r'_1(0)\times r'_2(1)=\times =

The equation of tangent at point P(4,1,4) is given by

30(x-4)-16(y-1)+18(z-4)=0

30x-120-16y+16+18z-72=0

30x-16y+18z=176

15x-8y+9z=88

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