Question

A cargo ship left port a and is headed across the ocean to shipping port b. After one month, the ship stopped at a refueling station along a path described by a vector with components leftanglebracket 14, 23 rightanglebracket. After another month, on the same path, the ship reached port b, twice the distance from port a as the fueling station. What are the characteristics of the vector representing the path of the ship?.

Answer 1

Explanation:

The vector representing the path of the ship from port A to the refueling station has components <14, 23>, and the vector representing the path from the refueling station to port B has twice the magnitude as the vector from port A to the refueling station.

To find the characteristics of the vector representing the path of the ship from port A to port B, we can add the two vectors together.

The sum of two vectors <a, b> and <c, d> is given by <a+c, b+d>. Therefore, the vector representing the path of the ship from port A to port B is given by:

<14, 23> + 2*<14, 23> = <14+214, 23+223> = <42, 69>

The vector representing the path of the ship from port A to port B is <42, 69>. This vector has a magnitude of √(42^2 + 69^2) = √(1764 + 4761) = √(6525) = 81 and a direction given by the angle theta, where tan(theta) = 69/42.

I hope this helps! Let me know if you have any other questions.

Answer 2

Answer: D. components:LeftAngleBracket 28, 46 RightAngleBracket, magnitude: 53.85

Explanation: