Question

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

Answer 1

Answer:

(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