Prove that the vectors `vec(A) = hat(i) + 2 hat(j) + 3 hat(k)and vec(B) = 2 hat(i) - hat(j)` are perpendicular to each other .

Explanation

Given : `vec(A) = hat(i) + 2 hat(j) + 3 hat(k)`
`vec(B) = 2 hat(i) - hat(j)`
`vec(A) * vec(B) = (hat(i) + 2 hat(j) + 3 hat(k)) * ( 2 hat(i) - hat(j) + o hat(k))`
`= 1 xx 2 + 2xx (-1) + 3 xx 0 = 0 `
Hence `vec(A)` is perpendicular to `vec (B)`