Equations of Planes

What type of equations define the plane given by the following:

x = 1 + 3s -3t

y = 7 - 7s + 2t

z = 2 - 3s + 4t

• vector equations

• parametric equations

• scalar equations

What type of equation defines the plane given by:
 $\overrightarrow{r\ }=\left[1,\ 7,\ 2\right]+s\left[3,\ -7,\ -3\right]+t\left[-3,\ 2,\ 4\right]$  

• vector equation

• parametric equation

• scalar equation

What type of equation defines the following plane given by:

3x + 5y + 2z - 13 = 0

• parametric equation

• vector equation

• scalar equation

In the equation of a plane given by: 3x + 5y + 2z - 13 = 0,

which vector below would be a normal to the plane?

• [3, 5, 2]

• [3, 0, -2]

• [5, 2, -13]

• [3, -5, 2]

If it was necessary to convert  $\overrightarrow{r\ }=\left[3,\ 4,\ 1\right]+s\left[1,\ 2,\ 3\right]+t\left[-4,\ -5,\ 6\right]$  

to scalar form, you would need to determine a normal to this plane by computing the cross product of what two vectors?

• [3, 4, 1] and [1, 2, 3]

• [1, 2, 3] and [-4, -5, 6]

• [3, 4, 1] and [-4, -5, 6]

• any two vectors in the equation could determine a normal

What is wrong with the following "equation" of a plane:
 $\overrightarrow{r}=\ \left[0,\ 3,\ -5\right]+s\left[6,\ -2,\ -1\right]+t\left[12,\ -4,\ -2\right]$  

• There is one too many direction vectors

• The direction vectors are collinear

• The direction vectors are non-collinear

• There is nothing wrong with this equation, it's legit!

In the equation of a plane given by:  $\overrightarrow{r}=\left[1,\ 3,\ -2\right]+s\left[-3,\ 4,\ -5\right]+t\left[9,\ 2,\ -1\right]$  , 

how are 's' and 't' defined?

• s and t are direction vectors

• s and t are position vectors 

• s and t are parameters

How would you find the x-intercept of a plane?

• Set y = z = 0 and solve for x

• Set x = z = 0 and solve for y

• Set x = y = 0 and solve for z

In 2D, a scalar equation defines a:

• plane

• line

• vector

In 3D, a scalar equation defines a:

• line

• plane

• vector