Describe the translation 7 units to the left, 12 units up using a vector.

The magnitude of the vector is √ (7^2+12^2) = √ (49+144) = √193

The direction is α=arctan (y/x) = arctan (12/-7) ≈-59.74 however this is relative to the negative x-axis so we add 180° to get the standard angle ... 180-59.74=120.26°

So the vector is √193 @ 120.26°