Questions: 1. Use the given vectors to sketch the following: a. a + b b. a - b c. 3a - 2b

Use the given vectors to sketch the following: (the left vector is vector \( A \) and the right is vector \( B \))

Vector addition: \(\vec{a} + \vec{b}\)

To find \(\vec{a} + \vec{b}\), place the tail of \(\vec{b}\) at the head of \(\vec{a}\). The resultant vector is drawn from the tail of \(\vec{a}\) to the head of \(\vec{b}\).

Vector subtraction: \(\vec{a} - \vec{b}\)

To find \(\vec{a} - \vec{b}\), reverse the direction of \(\vec{b}\) to get \(-\vec{b}\), then add it to \(\vec{a}\) using the same method as vector addition.

Scalar multiplication and vector subtraction: \(3\vec{a} - 2\vec{b}\)

First, scale \(\vec{a}\) by 3 to get \(3\vec{a}\) and scale \(\vec{b}\) by 2 to get \(2\vec{b}\). Then, reverse the direction of \(2\vec{b}\) to get \(-2\vec{b}\) and add it to \(3\vec{a}\).

\(\boxed{\text{Sketch the vectors as described above.}}\)

\(\boxed{\text{Sketch the vectors as described above.}}\)

{"axisType": 3, "coordSystem": {"xmin": -10, "xmax": 10, "ymin": -10, "ymax": 10}, "commands": ["a + b", "a - b", "3a - 2b"], "latex_expressions": ["$\\vec{a} + \\vec{b}$", "$\\vec{a} - \\vec{b}$", "$3\\vec{a} - 2\\vec{b}$"]}