Question

Find the vectors t, n, and b at the given point. Given r(t) = (t², 2t³, t, 1, -2/3, -1), what are the vectors t, n, and b?

Answer 1

To find the vectors t, n, and b at a given point, we differentiate the given function r(t) with respect to t. The t-vector is (2t, 6t², 1, 0, 0, 0), the n-vector is (2t, 6t², 0, 0, 0, 0), and the b-vector is (0, 0, 0, 1, -2/3, 0).

Step-by-step explanation:

To find the vectors t, n, and b, we need to differentiate the given function r(t) = (t², 2t³, t, 1, -2/3, -1) with respect to t. Let's differentiate each component separately:

t-vector:

t = (2t, 6t², 1, 0, 0, 0)

n-vector:

n = (2t, 6t², 0, 0, 0, 0)

b-vector:

b = (0, 0, 0, 1, -2/3, 0)