vector with a diagram

Question

A lighthouse is at the position of 7i - 3j , relative to the wharf. A boat is travelling in the direction parallel to 3i - j from the wharf. IF all measurements are in km, find to the nearest meter, the closest distance the boat will get to the lighthouse if it does not change directions.

State any assumption and effect of the assumption.


Can anyone please help me find the answer to this vector question with a diagram to assist?

Answer 1

by setting up a proportion 3/1 =7/x, we find the boat will be at position 7i - 7/3j which is north of the lighthouse. Therefore it can get closer and even hit the lighthouse if it follows a path parallel to 3i - j. The equation of the line for 3i - j has a slope = -1/3 and y intercept = 0

If you translate the line downward about 662 meters, and the boat follows this parallel line, it will hit the lighthouse. Or maybe I'm misinterpreting the question.