Question

# Determine whether the given vectors are orthogonal, parallel,or neither: u=(-3,\ 9,\ 6) v=(4,\ -12,\ -8)

Determine whether the given vectors are orthogonal, parallel,or neither:
$$u=(-3,\ 9,\ 6)$$
$$v=(4,\ -12,\ -8)$$

2021-06-10
Step 1
We first check the dot product of "u" and "v" to determine if they are orthogonal ( dot product will be 0 ):
$$u\times v=(-3)\times(4)\div(9)\times(-12)\div(6)\times(-8)=-168\neq0$$
so that these vectors are NOT orthogonal. We nextdetermine if "u" and "v" arelinearly dependent:
$$\frac{(-3)}{(4)}=-\frac{3}{4}$$
$$\frac{(9)}{(-12)}=-\frac{-3}{4}$$
$$\frac{(6)}{(-8)}=-\frac{3}{4}$$
Hence, these vectors are linearly dependent and arethus parallel:
Vectors "u" and"v" Are PARALLEL