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:
\(u=(-3,\ 9,\ 6)\)
\(v=(4,\ -12,\ -8)\)

Expert Answers (1)

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
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