A treasure map you uncovered while vacationing on the Spanish Coast reads as follows: "If me treasure ye wants, me hoard ye'll have, just follow thee directions these. Step to the south from Brisbain's Mouth, 6 paces through the trees. Then to the west, 10 paces ye'll quest, with mud as deep as yer knees. Then 3 paces more north, and dig straight down in the Earth, and me treasure, take it please." What is the displacement vector from Brisbain's Mouth to the spot on the Earth above the treasure? Consider east the positive x direction and north the positive y direction.
(-10, -2)
-2 is wrong
To find the displacement vector from Brisbane's Mouth to the spot above the treasure, you need to break down the directions given in the treasure map into their components and then sum them up.
Let's start by assigning coordinates to the starting point, Brisbane's Mouth. For simplicity, we can assume Brisbane's Mouth to be at (0,0) on a coordinate plane, where the positive x-direction is east and the positive y-direction is north.
According to the map, the first step is to go south 6 paces. Since going south means moving in the negative y-direction, the first step can be represented as (0, -6).
The second step is to go west 10 paces. Moving west means moving in the negative x-direction, so the second step can be represented as (-10, 0).
The final step is to go 3 paces north. Moving north means moving in the positive y-direction, so the final step can be represented as (0, 3).
To find the displacement vector, we need to sum up these individual steps. Adding the x and y components separately, we get:
Displacement vector = (0 + (-10) + 0, -6 + 0 + 3)
= (-10, -3)
Therefore, the displacement vector from Brisbane's Mouth to the spot above the treasure is (-10, -3).