MES Links
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MES Links
Determining Parallel and Perpendicular Vectors and Planes via the Cross and Dot Products https://youtu.be/_MHe1u2tqv8 In this video I review how to determine whether two vectors or planes are parallel or perpendicular. Two vectors are parallel of their cross…
Determining if 3 Points Lie on the Same Line Using the Cross Product https://youtu.be/S1khfWCF1u4

In this video I go over a method for determining if 3 points lie on the same line by using the cross product of any 2 position vectors formed from the points. If the cross product is zero then the points all lie on the same line.

#math #science #geometry #STEM #education
MES Links
Determining if 3 Points Lie on the Same Line Using the Cross Product https://youtu.be/S1khfWCF1u4 In this video I go over a method for determining if 3 points lie on the same line by using the cross product of any 2 position vectors formed from the points.…
Four Points are on a Plane if the Scalar Triple Product is Zero https://youtu.be/wjLcU4VIGFE

In this video I illustrate a method for determining of 4 points lie on the same plane by checking if their scalar triple product (or volume of a parallelepiped) is zero. If it is zero then it means the volume of the parallelepiped spanned by the position vectors between the 4 points is zero, aka a flat plane.

#math #science #geometry #education #STEM
MES Links
Distance from a Point to a Line using the Cross Product https://youtu.be/-ie6FTLTH0E In this video I go over a method for determining the shortest distance between a point and a line in 3D by using the length of the cross product and the area of a parallelogram.…
Distance from a Point to a Plane using the Dot Product https://youtu.be/-V6F0OpS5M8

In this video I go over a quick recap on the formula for determining the shortest distance between a point and a plane in 3D. The formula is just the projection of any position vector from the plane to the point onto the normal vector of the plane, and involves their dot product.

#math #science #geometry #STEM #education
MES Links
Distance from a Point to a Plane using the Dot Product https://youtu.be/-V6F0OpS5M8 In this video I go over a quick recap on the formula for determining the shortest distance between a point and a plane in 3D. The formula is just the projection of any position…
Distance Between Intersecting Lines, Parallel Lines, and Skew Lines https://youtu.be/hWqpXXNZK0U

In this video I discuss how to determine the distance between two lines for each of the 3 possible cases: intersecting lines, parallel lines, and skew lines (which don't intersect and are not parallel).

#math #science #geometry #education #STEM
MES Links
Traces of a Surface: Review and Example on an Ellipsoid whose Traces are Ellipses https://youtu.be/w72pnqHHbAA In this video I review traces of a surface, which are curves of intersection of a surface with planes parallel to the coordinate (x, y, z) planes.…
Equations of the Six Types of Quadric Surfaces https://youtu.be/0pCWT-FbmuY

In this video I review the standard form equations of the 6 types of quadric 3D surfaces: ellipsoid, cone, elliptic paraboloid, hyperboloid of one sheet, hyperbolic paraboloid, and hyperboloid of two sheets.

#math #science #geometry #education #STEM
MES Links
Cell Theory: Introduction and Fertilization https://youtu.be/idz5hM8dAqg In this video I go over a brief introduction into cell theory, which states that all living things are composed of one or more cells, and in multicellular organisms, every cell is derived…
Cell Structure and Organelles of Animal and Plant Cells https://youtu.be/_0Qofjy4m0c

In this video I go over the typical cell structures of animal and plant cells as well as the many organelles that comprise them. Both cells contain a nucleus with most of the organism's genome, besides the mitochondrial DNA in animals and plastid DNA in plants.

#science #biology #STEM #education #animals