Answer:
15 units NE
Step-by-step explanation:
Assuming the coordinate plane is a compass with N being the positive y-axis, we can use the Pythagorean theorem to find the magnitude of the vector. Since the vector is going up by 12 and right by 9 at the same time, it should form a diagonal line, aka the hypotenuse of a triangle. This triangle has both of its leg units as 12, and 9. Pythagorean theorem states that a^2 + b^2 = c^2, that is both of their legs squared is the hypotenuse of the triangle squared. 12^2 + 9^2 = c^2. c = 15. Now that we know the magnitude, let's go back to the quadrants as the compass. Since both units are positive, the vector goes in the positive direction on both sides, which is Quadrant 1. North and East would be the appropriate say for the vector's direction, thus the vector's direction will be 15 units North East.