Midterm 1 Calc 3

Front 1

Back 1

Ellipsoid

Front 2

Back 2

Cone

Front 3

Back 3

Elliptic Paraboloid

Front 4

Back 4

Hyperboloid of One Sheet

Front 5

Back 5

Hyperbolic Paraboloid

Front 6

Back 6

Hyperboloid of Two Sheets

Front 7

The angle between two planes

Back 7

Front 8

Finding the equation of a plane when given three points

Back 8

Find two vectors using the points.
Find the cross product of the two.

Then take your P initial and find a vector between that and arbitrary point XYZ.
Take the result of the cross product against that arbitrary vector and set equal to 0 and solve.

Front 9

Finding out if lines are parallel, skew, or intersecting

Back 9

Use the cross product equal to zero to find out if they are parallel.
Test for intersection by setting the values equal to each other and solve for T then plug back in to see if there's a solution

Front 10

Finding the equation of a plane when given a point and normal vector.

Back 10

Find directional vector between your initial P and an arbitrary XYZ. Dot against the normal and set equal to zero. Solve.