Rog_Sec_12_5

# Rog_Sec_12_5 - (8/5/08) Math 20C. Lecture Examples. Section...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (8/5/08) Math 20C. Lecture Examples. Section 12.5. Planes in three space † A vector n = ( a, b, c ) is said to be perpendicular or normal to a plane in xyz-space if it is perpendicular to all lines in the plane (Figure 1). n is perpendicular to all lines in the plane. FIGURE 1 (The point Q = ( x, y, x ) is in the plane if and only if n ·-→ PQ = 0. Theorem 1 The plane through the point P = ( x , y , z ) and perpendicular to the nonzero vector n = ( a, b, c ) has the equation, a ( x- x ) + b ( y- y ) + c ( z- z ) = 0 . (Proof: The point Q = ( x, y, x ) is in the plane if and only if n ·-→ PQ = 0.) Example 1 Give an equation of the plane through the point (2 , 3 , 4) and perpendicular to the vector (- 6 , 5 ,- 4 ) . Answer:- 6( x- 2) + 5( y- 3)- 4( z- 4) = 0 Example 2 Give an equation for the plane through (6 , 10 ,- 3) and perpendicular to the line x =- 3 t, y = 6 + t, z = 4- 7 t ....
View Full Document

## This note was uploaded on 08/31/2011 for the course MATH 20C taught by Professor Helton during the Spring '08 term at UCSD.

Ask a homework question - tutors are online