Calculus Parametric

Question

Find parametric equations x,y,z for the line using t variable (2t^2)i +(5t-3)j +(3t^3)k

Answer 1

Hi Al!

Parametric equations are really interesting. For 3-dimensional equations, each component is equivalent to the x, y, and z directions.

For example, imagine you are given the following line: (t - 1)i + (3t)j + (-4t^2)k. This aligns directly with (x)i + (y)j +(z)k. Given that, we can now set each component equal to its corresponding variable.

Coefficients of i : x = t - 1

Coefficients of j: y = 3t

Coefficients of k: z = -4t^2

I hope that helps!