Q1: Which of the following sets does not describe a line in the plane?

A1: $$\left{ \binom{x}{y} \in \mathbb{R}^2 ~\bigg|~ x + y = 2 \right} $$

A2: $$\left{ \binom{x}{y} \in \mathbb{R}^2 ~\bigg|~ x = 2 \right} $$

A3: $$\left{ \binom{x}{y} \in \mathbb{R}^2 ~\bigg|~ y = 2 \right} $$

A4: $$\left{ \binom{x}{y} \in \mathbb{R}^2 ~\bigg|~ x^2 + y^2 = 2 \right} $$

A5: $$\left{ \binom{x}{y} \in \mathbb{R}^2 ~\bigg|~ x^2 = 0 \right} $$

Q2: What is not a possible normal vector $\mathbf{n}$ for the line $$\left{ \binom{x}{y} \in \mathbb{R}^2 ~\bigg|~ x = 2 \right} $$

A1: $$ \mathbf{n} = \binom{1}{0} $$

A2: $$ \mathbf{n} = \binom{0}{1} $$

A3: $$ \mathbf{n} = \binom{-2}{0} $$

Q3: Does the line $$\left{ \binom{x}{y} \in \mathbb{R}^2 ~\bigg|~ x = 2 \right} $$ go through the origin?

A1: Yes!

A2: No!