Question: how to prove that two vectors are perpendicular to each other?
Answer: If the dot product two vectors is 0, they are orthogonal; in other words, they are perpendicular. The dot product between two vectors →u,→v is given by →u⋅→v=|→u||→v|cos(θ), so →u⋅→v=0⟹cosθ=0⟹θ=π/2(90∘).