determine the unit vector normal to the plane
Answers
Answer:
Explanation:
A unit vector is a vector of length 1. Any nonzero vector can be divided by its length to form a unit vector. Thus for a plane (or a line), a normal vector can be divided by its length to get a unit normal vector.
Example: For the equation, x + 2y + 2z = 9, the vector A = (1, 2, 2) is a normal vector. |A| = square root of (1+4+4) = 3. Thus the vector (1/3)A is a unit normal vector for this plane. Also, (-1/3)A is a unit vector.
Unit normal vectors: (1/3, 2/3, 2/3) and (-1/3, -2/3, -2/3)
Exercise: Find a unit normal vector for the plane with equation -2x -4y -4z = 0. How is this related to the example? Could you use the example to find the unit normal in this case?
Exercise on Lines in the Plane: Continuing with line m with equation 2x + 3y = 6, find the unit normal vectors for this line. Also, find a unit normal vector for line OA. Look for relationships.