Equations of Lines (8.1)

Which of these is the vector equation for a line in 2D?

• $\left[x,y\right]=\left[x_0,y_0\right]+t\left[m_1,m_2\right]$

• $y=mx+b$

• $Ax+By+C=0$

• $\left[x,y\right]=\left[x_0,y_0\right]+t\left[m_1,m_2\right]+s\left[n_1,n_2\right]$

In $\vec{r}=\vec{r_0}+t\vec{m}$ , what does the  $\vec{m}$  represent?

• A position vector to a known point on the line

• A position vector to an unknown point on the line

• A direction vector of the line (parallel to the line)

• A normal vector (perpendicular to the line)

In $\vec{r}=\vec{r_0}+t\vec{m}$ , what does the  $\vec{r_0}$  represent?

• A position vector to a known point on the line

• A position vector to an unknown point on the line

• A direction vector of the line (parallel to the line)

• A normal vector (perpendicular to the line)

In $\vec{r}=\vec{r_0}+t\vec{m}$ , what does the  $\vec{r}$  represent?

• A position vector to a known point on the line

• A position vector to an unknown point on the line

• A direction vector of the line (parallel to the line)

• A normal vector (perpendicular to the line)

What is an equation of a line that contains the point $\left(3,4\right)$  and has direction vector  $\left[1,2\right]$  ?

•  $\vec{r}=s\left[1,2\right]+t\left[3,4\right]$  

•  $\vec{r}=\left[1,2\right]+t\left[3,4\right]$  

•  $\vec{r}=\left[3,4\right]+t\left[1,2\right]$  

•  $\vec{r}=\left(3,4\right)+t\left[1,2\right]$  

What is the direction vector of the line $\vec{r}=\left[5,\ 0,\ 2\right]+t\left[1,\ 0,\ 0\right]$  ?

•  $\left[1,\ 0,\ 0\right]$  

•  $\left[0,\ 1,\ 1\right]$  

•  $\left[5,\ 0,\ 2\right]$  

•  $\left[0,\ 5,\ 0\right]$  

What is a possible direction vector of a line that contains the points  $A\left(8,\ -2\right)$   and  $B\left(3,\ 1\right)$  ?

•  $\left[8,\ -2\right]$  

•  $\left[5,\ -3\right]$  

•  $\left[3,\ 1\right]$  

•  $\left[11,\ -1\right]$  

What is a possible POSITION vector for a line that contains the points $A\left(8,\ -2\right)$ and $B\left(3,\ 1\right)$ ?

• $\left[8,\ -2\right]$

• $\left[5,\ -3\right]$

• $\left[3,\ 1\right]$

• not enough info to determine

What is a possible direction vector of a line that contains the points  $P\left(2,\ 0,\ 3\right)$   and  $Q\left(4,\ 4,\ 1\right)$  ?

•  $\left[-2,\ 4,\ 2\right]$  

•  $\left[4,\ 4,\ 1\right]$  

•  $\left[2,\ 4,\ -2\right]$  

•  $\left[2,\ -4,\ -2\right]$  

What is a possible equation of a line that contains the points $R\left(5,\ -2\right)$  and  $S\left(0,4\right)$  ?

•  $\left[x,y\right]=\left[5,-2\right]+t\left[5,-6\right]$  

•  $\left[x,y\right]=\left[0,\ 4\right]+t\left[5,\ 6\right]$  

•  $\left[x,y\right]=\left[0,\ 4\right]+t\left[5,\ -2\right]$  

•  $\left[x,y\right]=\left[5,-6\right]+t\left[5,\ -2\right]$