Question

vector A +vector B =vector R
vector A2 +vector B2 =vector R2
find the angle between the two vectors

Answer 1

vector A² = dot product of A with A =  | A |²
| A | is the magnitude of vector A.

$\vec{A} + \vec{B} = \vec{R}$

|R|² =  |A|² + | B |² + 2 | A | * |  B | * Cos θ
         where θ = angle between A and B.
As  |R|² = |A|² + |B|²,    Cos θ = 0    =>  θ = π/2

So the two vectors are perpendicular to each other.