Question

The position of the particle moving in space at time t ≥ 0 is r(t) = (2 + 2 cos(t))i − 2 sin(t)j + (3 − t π )k. Find the first time moment t0 such that the velocity vector v(t0) is orthogonal to the vector i − j.

Answer 1

Answer:

t0 = π/4

Step-by-step explanation:

The velocity v(t) = r'(t) = <-2sint,-2cost>

Since <1,-1>⊥v, <1,-1>•v=0. So,

(1)(-2sint) + (-1)(-2cost) = 0

cost - sint = 0