Lines and Planes in 3-space

Every line in 3-space must have a _______________ vector.

Every plane in 3-space has a __________ vector.

Which cases below allow us to construct an equation of line ( $L_1$ ) in 3-space?

• Given 2 points on $L_1$ 

• Given 1 point on $L_1$ and 1 direction vector

• Given another line that is parallel to $L_1$ 

• Given 3 points on $L_1$ 

In which case scenarios below, we can form plane equation ( $P_1$ ) in 3-space? 

• Given a point on the plane and normal vector of the plane

• Given 2 points on the plane

• Given 2 direction vectors on the plane

• Given a point on the plane and another plane that is parallel to $P_1$  

• Given a point on the plane and a line that is perpendicular to  $P_1$  

If two lines in 3-space are not parallel and do not intersect, they are called ___________ lines.

Select the correct way to find the intersection between two planes.

• Solving simultaneous equations

• Gaussian Elimination or Gauss Jordan

• Concept of determinant

• Inverse of coefficient matrix method

If a line is found to be perpendicular to two planes, then the two planes are said to be _____________ .

• parallel to each other

• orthogonal to each other

• no relationship at all

What do you think we could form if we have three points from 3-space?

• A 3D line

• A 3D plane

• A 3D triangle

• A 3D love-shape