Answer:
[tex]s=\pm 1[/tex]
Explanation:
The dot product of two vectors [tex]\vec{a}=a_1\vec{x}+b_1\vec{y}[/tex] and [tex]\vec{b}=a_2\vec{x}+b_2\vec{y}[/tex] is given by
[tex]\vec{a}\cdot\vec{b}=a_1\cdot a_2+b_1\cdot b_2[/tex]
The dot product of two orthogonal vector is always zero thus if [tex]\vec{a}=\vec{x}+s\vec{y}[/tex] and [tex]\vec{b}=\vec{x}-s\vec{y}[/tex], their dot product would be
[tex]\vec{a}\cdot\vec{b}=1\times1+s\times-(s)=1-s^2=0[/tex]
[tex]\implies 1-s^2=0[/tex]
[tex]\implies s^2=1[/tex]
[tex]\implies s=\pm 1[/tex]
