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.enter image source here enter image source here

1 Answer
Jan 12, 2018

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