Question

Prove two non-zero vectors a and b are orthogonal if and only if a ⋅ b = 0.

Answer 1

Given : Vectors a and b

a, b are not equal to zero

To prove: a and b are orthogonal

Proof

STEP 1: Scalar or Dot product of vectors a and b.

a.b = a×b×Cos(x)

where x is angle between a and b

Step 2: a.b=0

a×b×Cos(x)=0

Now a, b are not equal to zero

i.e, Cos(x) = 0

=> x = 90°

Therefore, a and b are orthogonal

Hence, proved