Question

How solve it?

The final test for occupying the vacancy of an aeroplane controller consists of interpreting the flight vector of an aeroplane expressed in the figure.
In Cartesian Coordinates: Determine the vector needed to meet the test correctly.

Answer 1

b) -28 i + 28`sqrt(3)` j

P.S. b) is true considering that your teacher forgot to add "i" after -28. See explanation.

Explanation:

First, you can just look at the given options and eliminate a) and d). Since the vector is in the second quadrant, you know that the x value must be negative, and that the y value must be positive.

Secondly, you know that the angle is 30° FROM the positive y-axis. You know that if the angle is 45°, then x and y have the same value. Since your angle is less than 45°, you know that your y value will be greater than your x value.

In b) we have:
x = -28
y = 28`sqrt(3)`

Only looking at the magnitude of the vector (the length), we know that y > x, because 28`sqrt(3)` > 28 (here we don't care about the negative sign in front of the x value, because we are only looking at the magnitude).

In c) we have:
x = -28`sqrt(3)`
y = 28

Here, we have y < x, because 28 < 28`sqrt(3)` (again here we don't care about the negative sign in front of the x value, because we are only looking at the magnitude).

Since we knew from our initial analysis that y > x, c) is false and b) is true.

P.S. b) is true considering that your teacher forgot to add "i" after -28.

-28 + 28`sqrt(3)` j should be -28 i + 28`sqrt(3)` j