Determine if the following vectors are orthogonal A6 2 1 and

Determine if the following vectors are orthogonal: A=(6 2 -1) and B=(2 -7 -2)

Given that

A = (6 2 -1) and B = (2 -7 -2)

We know that

If two vectors are said to be orthogonal then their dot product equal to zero

Dot product of (a₁,a₂,a₃) and (b₁,b₂,b₃) is ,

(a₁,a₂,a₃) . (b₁,b₂,b₃) = a₁b₁ + a₂b₂ + a₃b₃

Hence ,

A.B = (6 2 -1) . (2 -7 -2) = (6.2) + (2.(-7)) + ((-1).(-2))

= 12 + (-14) + 2

= 12 - 14 + 2

= 14 - 14

(6 2 -1) . (2 -7 -2) = 0

A.B = 0

Dot product of A(6 2 -1) , B(2 -7 -2) is 0

Therefore ,

The two vectors A and B are orthogonal