True-False Quiz Questions 22: Cauchy–Schwarz Inequality https://youtu.be/5SF6JokcFUY

In this video I show that the absolute value of the dot product has a maximum value of the lengths of each vector multiplied by each other. This relation is known as the Cauchy-Schwarz Inequality.

#math #science #STEM #vectors #education

True-False Quiz Questions 19 to 21: When Dot and Cross Products Equal Zero https://youtu.be/naNwDZdYSZY

In this video I show that if the dot or cross products are zero then neither vector has to be zero, but if BOTH the dot and cross products are zero then at least one of the vectors has to be zero.

True-False Quiz Questions 17 and 18: Circular and Parabolic Cylinders in 3D https://youtu.be/Lad3PGhkwd4

In this video I show that a formula has different meanings when plotted in 2D vs 3D, such as the equation of a circle in 2D which becomes a circular cylinder in 3D.

True-False Quiz Questions 15 and 16: Perpendicular Vectors to a Plane https://youtu.be/_PcU6fKN0sc

In this video I quickly show that a vector is perpendicular to a plane if it is a multiple of the normal vector obtained from the plane's linear equation.

True-False Quiz Questions 13 and 14: Dot and Cross Products with Repeating Vectors https://youtu.be/N2HVNiix8eI

In this video I show two interesting formulas involving the dot and cross products in which a vector is used twice.

#math #science #STEM #geometry #education

True-False Quiz Questions 10 to 12: Rearranging Scalar and Vector Triple Products https://youtu.be/IHwBfOrJG_A

In this video I show that interchanging the vectors in the scalar triple product result in the same answer but not when doing so for the vector triple product. I also show that adding vectors before taking a cross product is equivalent to taking two cross products and adding them up.