Question

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)

Answer 1

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)