Find parametric equations for the tangent line to the curve with parametric equations $x = 9 t$, $y = 7 t ^ { 2 } , z = 4 t ^ { 3 }$ at the point with $t = 1$. Select the correct answer.
A) $x = 9 + 9 t , y = 7 + 14 t , z = 4 + 12 t$
B) $x = 9 + 9 t , y = 7 + 7 t , z = 4 + 4 t$
C) $x = 1 + 9 t , y = 1 + 7 t , z = 1 + 4 t$
D) $x = 1 + 9 t , y = 1 + 14 t , z = 1 + 12 t$

Question

Quizplus · Accepted Answer

The parametric equations of the tangent line are given by the position vector of the point plus the scalar multiple of the tangent vector. At the point with $t = 1$, the position vector is $${\bf r}(1) = 9{\bf i} + 7{\bf j} + 4{\bf k}$$and the tangent vector is $${\bf r}'(1) = 9{\bf i} + 14{\bf j} + 12{\bf k}.$$Therefore, the parametric equations of the tangent line are $$x = 9 + 9 t, \quad y = 7 + 14 t, \quad z = 4 + 12 t.$$

Find Parametric Equations for the Tangent Line to the Curve x=9tx = 9 tx=9t

Find Parametric Equations for the Tangent Line to the Curve $x = 9 t$