Question

how can you deduce that two vectors are perpendicular

Answer 1

suppose two vector are A and B.
then,
A • B = 0
implies
A is perpendicular to B

Answer 2

Let a vector and b vector be two given vectors.

If the dot product of these two vectors are equal to zero, then they are said to be orthogonal to each other.

That is, a vector . b vector = 0, then they are said to be perpendicular vector.

It can be proved as,

Dot products of two vectors is given by, a vector . b vector = |a vector||b vector| cos ϴ ... (1)

The equation will become 0, only When ϴ = 90°

Cos ϴ =0

Hence equation (1) becomes, a vector . b vector = |a vector||b vector| (0) = 0

Hence from the deduction, if a vector .  b vector = 0, then the two vector make 90° angle between them.