New: vectorsAll contenthive-129948krhive-196917steemzzanhive-183959hive-180932hive-166405hive-185836uncommonlabphotographyhive-183397hive-101145hive-150122hive-144064hive-145157hive-188619bitcoinkrsuccesshive-184714lifehive-139150hive-103599hive-109690hive-180301TrendingNewHotLikersmes (67)in hive-196037 • last yearDistance From a Point to a Plane + ProofIn this video I derive the formula for the distance between a point to a plane in 3D coordinates. The distance formula can be derived by taking the scalar projection of a vector from a point on the…mes (67)in hive-196037 • last yearIntersection of Planes Forms a LineIn this video I show that two non-parallel planes form a line of intersection and show how to determine its equation. I also show the reverse procedure as well, that is, if we are given an equation…mes (67)in hive-196037 • last yearParallel and Non-Parallel Planes + ExampleIn this video I go over parallel and non-parallel planes and go over an example on finding the angle between two non-parallel planes. Two planes are parallel if their normal vectors are parallel. If…mes (67)in hive-196037 • last yearLinear Equation of a Plane + ExamplesIn this video I go over the linear equation of a plane, which involves rewriting and simplifying the scalar equation of a plane. I do this by starting with the scalar equation of a plane and then…mes (67)in hive-196037 • last yearVector and Scalar Equations of a PlaneIn this video I go over planes in 3D and derive the vector equation of a plane and then convert that into scalar equations of a plane. A plane can be described by a point on the plane and a vector…mes (67)in hive-196037 • last yearExample on Skew Lines: Lines that Aren't Parallel and Don't IntersectIn this video I go over an example on determining whether 2 lines with given parametric equations are skew lines; which are lines that do not intersect and are not parallel. By looking at the…mes (67)in hive-196037 • last yearVector Equation of a Line SegmentIn this video I go over the vector equation of a line segment instead of the entire line. I first start off with an example involving parametric equations and noting that setting the parameter t = 0…mes (67)in hive-196037 • last yearDirection Numbers and Symmetric Equations of a LineIn this video I go over what direction numbers and symmetric equations of a line are. Direction numbers are the components of the parallel vector in a vector equation of a line. We can use any three…mes (67)in hive-196037 • last yearParametric Equations of a LineIn this video I convert the vector equation of a line into its parametric equations form. To do this I first expand the vector equation by writing out its components and then summing them up. Then I…mes (67)in hive-196037 • last yearVector Equation of a LineIn this video I go over the vector equation of a line in 3D space. The method is similar to that of a line in 2D using the point-slope method. In 2D, a line is determined when a point on the line…mes (67)in hive-196037 • 2 years agoDistance Formula in 2D and 3D and Their ProofsIn this video I prove the distance formula between 2 points in both two and three dimensions. The distance formula in 2D is readily derived using the Pythagorean theorem. In 3D we can extend the 2D…mes (67)in hive-196037 • 2 years agoGraphing the y = x Plane in 3D CoordinatesIn this video I go over a short example on graphing the equation y = x in three dimensions. The surface is just a vertical plane that is split directly between the x- and y-axes. This video was…mes (67)in hive-196037 • 2 years agoCircle and Cylinder in 3D CoordinatesIn this video I go over an example on graphing a circle and a cylinder in 3D coordinates. The circle that I graph has the equation x2 + y2 = 1 and z = 3. This means that the circle is centered about…mes (67)in hive-196037 • 2 years agoVertical and Horizontal PlanesIn this video I go over graphing vertical and horizontal planes in 3D space. I start off with an example on plotting the equations z = 3 and y = 5. The first equation, z = 3, is just a horizontal…mes (67)in hive-196037 • 2 years agoVectors as Forces in Physics and EngineeringIn this video I go over applications of vectors in physics and engineering, and in particular look at "Forces". Since forces involve a magnitude (measured in pounds or newtons) and a direction, we…mes (67)in hive-196037 • 2 years agoUnit VectorsIn this video I go over unit vectors, which are vectors of length 1. Any vector "a" can be expressed as a unit vector "u" pointing in the direction of "a" by dividing the vector "a" by the length…mes (67)in hive-196037 • 2 years agoStandard Basis Vectors i, j, kIn this video I introduce standard basis vectors which are special vectors with a length 1 and point in the direction of the x, y, and z axis, and are labeled i, j, and k, respectively. Any vector…mes (67)in hive-196037 • 2 years agoProperties of VectorsIn this video I go over a list of 8 properties of vectors in terms of addition and scalar multiplication. I also provide algebraic proofs for properties 1 and 2. The remaining properties, however…mes (67)in hive-196037 • 2 years agoVector AlgebraIn this video I go over the addition, subtraction, and scalar multiplication of vectors but algebraically. This is done by treating each vector component separately and then applying basic algebraic…mes (67)in hive-196037 • 2 years agoThe Length or Magnitude of a VectorIn this video I go over a quick video to show the formula for the length or magnitude of a vector. This simply applying the distance formula, proved in my earlier video: and which is just a 3D…
