Equations of Lines and 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

• 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]

• [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

• 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!

• 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