Question

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

u = <7, -4>, v = <-28, 16>

Answer 1

to check if two vectors are orthogonal(perpendicular), simply check their dot product, if their dot product is 0, then they're perpendicular, let's check.


`\bf \ \textless \ 7,-4\ \textgreater \ \cdot \ \textless \ -28,16\ \textgreater \ \implies (7\cdot -28)+(-4\cdot 16)\implies -196-64 \\\\\\ \boxed{-264}\impliedby \textit{nope, no orthogonal}`

to check if two vectors are parallel, simply check their slope by doing a b/a check, if the slopes are the same, then they're indeed parallel to each other, let's check.


`\bf \textit{slope of \underline{u} }\cfrac{7}{-4}\implies \boxed{-\cfrac{7}{4}}\qquad \qquad \textit{slope of \underline{v} }\cfrac{-28}{16}\implies \boxed{-\cfrac{7}{4}}`

well, there you have it, the slopes are the same.