Vectors are basically multi-dimensional numbers. Velocity, Force, Torque, etc. are all vectors. Anything that has a magnitude (e.g. 30 mph) and a direction (e.g. NE) is a vector. On the other hand, a quantity with no direction is called a scalar (e.g. mass, temperature, time). In many physics equations, you have to multiply vectors. There are two ways, scalar (or dot) products and vector (or cross) product. The difference between the two is the dot product results in a scalar value (no direction) while a cross product results in a vector value (has direction). Dot products are used to determine things like work and energy. Cross products are used for things like torque, and magnetic fields. As a vector is inherently more complex than a scalar, equations with cross products are more complex to solve.
I hope that was helpful and not just a Charlie Brownish Wah Wah Wah Wu-Wah.
"Recollect me darlin, raise me to your lips, two undernourished egos, four rotating hips"
