Question

High level math: Use the formula for the dot product law to prove that if two vectors are perpendicular ( a perp. to b) then a x b = 0

Answer 1

if vectors a and b are perpendicular \[\vec a\times\vec b\neq0\]you maybe mean\[\vec a\cdot\vec b=0\]?

Answer 2

the second one you wrote

Answer 3

dot products are very different than cross products, so try not to confuse the two

Answer 4

the dot product is defined as\[\vec a\cdot\vec b=||\vec a||||\vec b||\cos\theta_{ab}\]where theta is the angle between vectors a and b
what is the angle between two perpendicular vectors?