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Dot product - Orthogonal

  • Thread starter vorcil
  • Start date
  • #1
393
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By evaluating the dot product,

find the values of the scalar s for which the two vectors
b=X+sY and c=X-sY
are orthogonal
also explain your answers with a sketch:





my working

(X,sY).(X,-sY) has to equal 0 for them to be orthogonal

x.x = 1 since they are unit vectors
sY.-sY = -1 to make the whole thing 0

s = 1
1*y . -1*y = -1

1-1 =0

sketch would be two vectors perpendicular to one another?
 

Answers and Replies

  • #2
393
0
could someone please inform me If my work is correct?
cheers
 
  • #3
33,521
5,199
(X + sY).(X - sY) = 0
==> X.X + sY.X - sX.Y -s2Y.Y = X.X - s2Y.Y = 0
==> 1 - s2 = 0

You found one solution for s; there are two.
 

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