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.

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.

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 of the 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).

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.

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.

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.