pedzenekO

2021-08-18

Determine whether the vectors u and v are parallel,
orthogonal, or neither.

$u=\u27e8-3,4\u27e9,v-\u27e8\frac{20}{15}\u27e9$

$u=\u27e8-3,4\u27e9,v-\u27e8\frac{20}{15}\u27e9$

pierretteA

Skilled2021-08-19Added 102 answers

Without finding the angle between two vectors, we can determine if they are parallel if they are scalar multiples of each other. If $u=kv{\textstyle \phantom{\rule{1em}{0ex}}}\text{or}{\textstyle \phantom{\rule{1em}{0ex}}}v=ku$ for non-zero value of k since we are simply scaling. The two vectors are orthogonal if their dot product is 0: $u\times v=0$

Check if they are parallel:

Since$v\ne 5u,\u27e820,15\u27e9\ne 5\u27e8-3.4\u27e9$

Then u and v are not parallel.

Check if they are orthogonal:

Find the dot product:

$u\times v=(-3)\left(20\right)+\left(4\right)\left(15\right)=-60+60=0$

Since$u\times v=0$ , then u and v are orthogonal.

Check if they are parallel:

Since

Then u and v are not parallel.

Check if they are orthogonal:

Find the dot product:

Since

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