10-5 Planes in Space

We already know what a vector in a three dimensional setting looks like:

A plane in space is the set of all points that satisfy the equation: Ax + By + Cz = D
It looks like:

To find a vector ,normal or perpendicular, to the plane Ax + By +Cz = D, just plug the coefficients A, B, and C into the vector formula:

EXAMPLE

• 
  
  given 3x - 8y + 5z = 24
• 
  
  plug 3, -8, and 5 into the vector formula
• 
  
  your answer should be

You can also determine a plane by using a normal vector and a point, as shown below:

courtesy of Mr. French

To find a plane using a normal vector and a point P:

• 
  
  Place the vector's tail at the point P =

• 
  
  Pick another point and draw another vector to that point

• 
  
  Find the displacement vector (head - tail) =

• 
  
  *the vectors are perpendicular so their sum is 0

• 
  
  Use algebra so that

• 
  
  Then, and that's your answer!

EXAMPLE

given and P = (2,5,-1)

• 
• 
• 
  

You will find that essentially, you only need the equation

These are pictures from a JACK'S MANNEQUIN concert I went to in February. They're my favorite band and everyone should go listen to their music. Their rooted from SOMETHING CORPORATE, which is my other favorite band, because the lead singer was originally from SoCo. Andrew McMahon, the lead singer, fought and beat cancer, which i think is amazing and he's amazing so everyone should go buy his music NOW!

JOEY YOU'RE UP NEXT!!!!