anonymous
  • anonymous
i'll use the tool excuse me,
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
a and b are vectors, a=(x1,y1) b=(x2,y2) \[\left| a \right|\left| b \right|=\left| adotb \right| \] then why x1y2-x2y1=0 ? please help me
anonymous
  • anonymous
plus they are not 0 vectors
hartnn
  • hartnn
have you tried this ? its just algebraic manipulations....

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hartnn
  • hartnn
if you know \( |a|= \sqrt{x_1^2+y_1^2}\) \( |b|= \sqrt{x_2^2+y_2^2}\) \(|a.b|=x_1x_2+y_1y_2\)
hartnn
  • hartnn
substitute these and square both sides, what you get ?
hartnn
  • hartnn
i see, since you have disappeared offline, i'll write down few steps. \((x_1^2+y_1^2)(x_2^2+y_2^2)= (x_1x_2+y_1y_2)^2\) Expand both sides, and you'll see \(x_1^2x_2^2+y_1^2y_2^2\) gets cancelled from both sides, what remains will give you \((x_1y_2-x_2y_1)^2=0\) which gives you required result.
anonymous
  • anonymous
thank you, @hartnn and sorry for disappearing i was using wrong aspects, which made me go nowhere. thanks again

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