[Math] For a curve, find the unit tangent vector and parametric equation of the line tangent to the curve at the given point

calculuscurvesparametricplane-curvestangent line

For the curve $r(t) = ti+tj+\sqrt{4-t^2}k$ find the unit tangent vector $T ( t )$ and parametric equation of the line tangent to the curve at the point $P(1,1,\sqrt{3}).$

I am not sure what exactly to do here. Any help or suggestion would be greatly appreciated. I think I know how to find the unit tangent vector but I don't know how to find the parametric equation.

Best Answer

Assuming you are right about knowing how to find $T(t)$( I believe in you, you can do it!) Recall that a line can be parameterized as $l(t)=v_0+tv$ where $v_0$ is a position point(i.e. the value of your function at the point you want to find the tangent) and $v$ the direction vector(i.e. the "slope" of your line, so the tangent to your curve at the desired point.)

Related Question