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anonymous
 one year ago
Determine whether the vectors u and v are parallel, orthogonal, or neither.
u = <6, 2>, v = <8, 24>
anonymous
 one year ago
Determine whether the vectors u and v are parallel, orthogonal, or neither. u = <6, 2>, v = <8, 24>

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jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1Let u = <a,b> v = <c,d> the dot product of u and v is u dot v = a*c + b*d if the dot product of u and v is 0, then u is orthogonal (ie perpendicular) to v.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0it is orthogonal, correct?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1u is parallel to v if and only if u = k*v for some scalar k u = k*v <a,b> = k*<c,d> <a,b> = <k*c,k*d> a = k*c and b = k*d k = a/c and k = b/d a/c = b/d All that work above shows that IF a/c = b/d, then u and v are parallel. They either point in the same direction, or they point in complete opposite directions.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1`it is orthogonal, correct?` yes that is correct u dot v = a*c + b*d u dot v = 6*8 + (2)*24 u dot v = 48 + (48) u dot v = 0 so they are indeed orthogonal
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