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Aloiza [94]
2 years ago
9

Find the values of t so that the tangent line to the given curve is contains the given point? Given r(t)=2ti+t^2j-t^2k at point

(0,-4,4)
Mathematics
1 answer:
Mariana [72]2 years ago
6 0

Answer:

t = -2,2

Step-by-step explanation:

The curve equation, r(t)=2ti+t^2j-t^2k

Let at t=a tangent to the curve.

Equation of tangent:  

L(k) = r(a) + k r'(a)

r(a)=

r'(t)=

Put t=a

r'(a)=

Equation of tangent:

L(k) =  + k

L(k)=

Tangent passing through (0,-4,4)

Therefore,

2a + 2k = 0   ⇒  k = -a

a^2+2ak=-4

a^2-2a^2=-4

-a^2=-4

a=\pm 2

At t = -2,2  tangent line to the curve passing through (0,-4,4)

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