MATH 20C Lecture 7

Relative Position Between Two Planes in ${\mathbb{R}}^3$

1. and are parallel or coincide. is parallel to . for some scalar .
2. If and are not parallel, then they intersect along a line. and are not parallel.

Relative Position Between a Line and a Plane in ${\mathbb{R}}^3$

1. is parallel to or is contained in . The direction vector of is orthogonal to the normal vector of .
2. If the line and plane are not parallel, then they intersect at a unique point.

13.1 Vector Valued Function

Curve/Space Curve

Can be represented as

• is called a parameter
• are called components or coordinate functions
• is called a vector parameterization of the space curve

Parameterize the Curve $C$ which is the intersection between $x^2-y^2=z-1,x^2+y^2=4$

is a vector parameterization of .

13.2 Limits

Limit of Vector-Valued Function

Let
The limit of the vector-valued function as is defined as

Continuous

is continuous at if

1. is continuous at iff all components are continuous at
2. If is continuous at all values of t in the domain, we simply say the function is continuous.