Question

Help. Submarine Hunting. Additional and Advanced Excerises chapter 12. Thomas' Calculus.

Answer 1

person A takes their small boat out onto the river and
anchors himself at a position of (4, 0,0) from the dock (origin). person B
rows out to a position of (0, 5, 0). Before they can get started with
their observations, person A accidentally tosses his laboratory
notebook in the water where it drops to a location of (2, -1,- 1/3).
After 4 seconds, each scientist observes the location of the notebook
from their current position. Person A sees it in the direction 2i+3j-1/3k
and Person B sees it as being in the direction 18i - 6j - k. Doing some
fast calculations, they realize they can move quickly enough to retrieve
the book 20 seconds from now. What position does one of them need
to move to in order to retrieve the book from the river?

Answer 2

Should just be the sum of the boat's position vector and position of the book relative to the boat. So for person A:
<4,0,0>+<2,3,-1/3>=<6,3,-1/3> will be the position (relative to the origin) that A needs to move to to retrieve the book.