Question

Suppose that a particle follows the path c(t)=(eᵗ,e⁻ᵗ,cos t) until it flies off on a tangent at t=1. Where is the particle in R³ at t=3?

Answer 1

The position of the particle in R³ at t=3 is (e³,-e³,cos 3) based on the given path c(t)=(eᵗ,e⁻ᵗ,cos t).

Step-by-step explanation:

To find the position of the particle in R³ at t=3, we need to find the position vector, r(t), of the particle at t=3. From the given path, we have c(t)=(eᵗ,e⁻ᵗ,cos t). To find r(t), we can substitute eᵗ for x, e⁻ᵗ for y, and cos t for z in the position vector r(t) = xi + yj + zk. Therefore, at t=3, the position of the particle in R³ is r(3) = (e³,-e³,cos 3).