Determine whether the given vectors are orthogonal, parallel, or neither. (a) a = 9, 6, b = - 4, 6 orthogonal parallel neither (b) a = 8, 7, - 3, b = 5, - 1, 7 orthogonal parallel neither (c) a = - 4i + 12j + 8k, b = 3i - 9j - 6k orthogonal parallel neither (d) a = 3i - j + 3k, b = 3i + 3j - 2k orthogonal parallel neither

(a) Orthogonal, (b) Neither, (c) Parallel, d (Orthogonal

Step-by-step explanation:

a and b are parallel is a=kb

a and b if a dot b = 0

(a) a dot b = (9) (-4) + 6 (6) = -36+36=0

a and b are orthogonal

(b) a dot b = 40-7-21=12

a=kb - > there is no k value satisfying the equation

a and b are neither parallel or orthogonal

(c) a dot b = - 12-108-48=-168

a=kb - > k=-3/4 satisfies the equation

a and b are parallel

(d) a dot b = 9-3-6=0

a and b are orthogonal