I have a question from my chapter on vectors:

Find the component form of the vector that represents the velocity of an airplane descending at a speed of 100 mph at and angle of $30^\circ$ below the horizontal.

For the angle of descent I calculated $0^\circ - 30^\circ = -30^\circ = 330^\circ$

The answer at the back of the book calculated the vector using $180^\circ + 30^\circ = 210^\circ$ so my answer was wrong.

But, wouldn't that vector have the airplane going backward? It seems to me the x component of the vector would be positive while the y component would be negative, putting it in Quadrant IV.

Where is my thinking wrong on this?

BTW, my answer was $v=\langle 50\sqrt{3}, -50 \rangle$ while the textbook says it should be $v=\langle -50\sqrt{3}, -50 \rangle$