What are the values of s that make two given vectors orthogonal?

[vorcil]

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?

 

[vorcil]

could someone please inform me If my work is correct?
cheers

 

[Mark44]

(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.