The Cross Product and its Useful Properties https://youtu.be/8GgG-1O_WvU

In this video I go over a review of the cross product, its definition and formulas, as well its many useful applications in mathematics and physics.

#math #science #education #geometry #STEM

Calculating Area of a Parallelogram and Volume of Parallelepiped with the Cross Product https://youtu.be/6wuT6abp-vo

In this video I show how the cross product can be used to determine the area of a parallelogram and the volume of a parallelepiped.

#math #science #education #geometry #STEM

Finding the Normal or Perpendicular Vector of a Plane https://youtu.be/As_Z3nqWk4Y

In this video I show that the cross product of two non-parallel vectors on a plane obtains a vector perpendicular to that plane, and is called the normal vector.

#math #science #education #STEM #geometry

Finding the Angle Between Two Intersecting Planes using the Dot Product of their Normal Vectors https://youtu.be/baRwDDtmwPY

In this video I show that we can determine the angle between two intersecting planes by computing the dot product of their normal or perpendicular vectors.

#math #science #education #geometry #STEM

Vector, Parametric, and Symmetric Equations of a Line https://youtu.be/ZeaSgJSWRuA

In this video I go over the the 3 main equations of a line in 3D: vector equation, parametric equations, and symmetric equations.

#math #science #education #STEM #geometry

Vector and Scalar Equations of a Plane https://youtu.be/DuSUIKAavcw

In this video I review the vector and scalar equations of a plane. The vector equation is the dot product set to equal zero between normal vector with the position vector of any two points on the plane. The scalar equation is the same as the vector equation except the dot product is evaluated, which produces a scalar (or number).

#math #science #education #STEM #geometry

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 product is zero, and are perpendicular if their dot product is zero. The angle between two planes can be determining the angle between their normal vectors: if the angle is zero then the planes are parallel.

#math #geometry #science #education #STEM

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

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

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.

#math #science #geometry #education #STEM