\[ \vec{v}+\vec{v}=\langle 0.21,14.03\rangle \] c. In what quadrant does the resultant vector lie?

First off, let's break down the given vector equation! You've got \(\vec{v} + \vec{v} = \langle 0.21, 14.03 \rangle\). Simplifying this, you can see that \(2\vec{v} = \langle 0.21, 14.03 \rangle\), which means \(\vec{v} = \langle 0.105, 7.015 \rangle\). Now, regarding the quadrant: The "x" component (0.105) is positive and the "y" component (7.015) is also positive. This places the resultant vector squarely in the first quadrant, where both x and y values are greater than zero. So, joyfully wave hello to Quadrant I! If you’re ever unsure about quadrant placement, just remember: Quadrant I is where the magic happens—with both positive x and positive y driving the party!