Find r'(t), r''(t), r'(t) · r''(t), and r'(t) × r''(t).

Question

r(t) = 3/2t²i - 5tj + 2/3t³k

(a)    r'(t) = ________

(b)    r''(t) = ______

(c)    r'(t) · r''(t) = ________

(d)    r'(t) × r''(t) = ________

Answer 1

r(t) = 3/2t²i - 5tj + 2/3t³k

for r'(t), derive the functions in front of i, j and k.

r'(t) = 3ti - 5j + 2t²k

r''(t) = 3i - 0j + 4tk

This vector function can also be written as:

r(t) = < 3/2t², 5t, 2/3t³ >

r'(t) = < 3t, 5, 2t² >

r''(t) = < 3, 0, 4t>

In this form it is easier to figure out the last two problems which ask you to complete the C) dot product and d) the cross product. These are difficult to explain in text. I would recommend looking at your class notes or textbook to find how to set up the dot product and the cross product of two vectors.

Again, feel free to message me if you would like to set up a time to go over vectors.