# OpenStax Calculus Dynamic Figures

- Page ID
- 7472

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

- Figure 12.2.7 Skew Lines
- Two skew lines in 3-space

- Figure 12.2.8 Interlocking circles
- Two interlocking circles in 3-space

- Figure 12.2.12 A Sphere Example
- The plot of an example sphere

- FIGURE 12.5.1
- Vector \(\vec{v}\) is the direction vector for \( \vec{PQ}\).

- FIGURE 12.5.5: Non-intersecting lines in space do no have to be parallel
- Given two lines in the two-dimensional plane, the lines are equal, they are parallel but not equal, or they intersect in a single point. In three dimensions, a fourth case is possible. If two lines in space are not parallel, but do not intersect, then the lines are said to be skew lines.

- EXAMPLE 12.5.8: FINDING THE LINE OF INTERSECTION FOR TWO PLANES
- Find parametric and symmetric equations for the line formed by the intersection of the planes given by \(x+y+z=0\) and \(2x−y+z=0\).

- Figure 14.4.3
- A Surface with No Tangent Plane at the Origin

- EXAMPLE 15.2.3
- The double integral in this example represents the volume of this 3D region. Note that in the \(z\)-direction, the units are in tens.

- EXAMPLE 15.2.4: DOUBLE INTEGRAL
- This double integral's value is the net result of the volume of the solid region between the surface and the region of integration in the \(xy\)-plane that is above the \(xy\)-plane and the negative of the volume of the solid region between the surface and the region of integration in the \(xy\)-plane that is below the \(xy\)-plane.

- Figure 16.1.6 Visualizing a 3D Vector Field
- Visualizing a 3D vector field

- EXERCISE 16.1.7: VISUALIZING A 3D VECTOR FIELD
- Visualizing a 3D vector field: Sketch vector field \(G(x,y,z)=⟨2,\dfrac{z}{2},1⟩\) by substituting enough points into the vector field to get an idea of the general shape.