Question

Find a vector parametrization of the curvex = -3 z^2in the xz-plane. Usetas the parameter in your answer.

\vec{r}(t) =

Answer 1

To find a vector parametrization of the curve, use the equation r(t) = -3t^2i + 0j + tk.

Step-by-step explanation:

To find a vector parametrization of the curve, we need to express the position vector in terms of a parameter. In this case, we can use t as the parameter. The given curve is x = -3z^2 in the xz-plane. Since there is no y component, we can write the position vector as:

r(t) = -3t^2ĵ + 0Ķ + tķ

Here, ĵ represents the unit vector along the x-axis, Ķ represents the unit vector along the y-axis, and ķ represents the unit vector along the z-axis.