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## anonymous 3 years ago i'll use the tool excuse me,

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1. 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

2. anonymous

plus they are not 0 vectors

3. hartnn

have you tried this ? its just algebraic manipulations....

4. hartnn

if you know $$|a|= \sqrt{x_1^2+y_1^2}$$ $$|b|= \sqrt{x_2^2+y_2^2}$$ $$|a.b|=x_1x_2+y_1y_2$$

5. hartnn

substitute these and square both sides, what you get ?

6. 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.

7. anonymous

thank you, @hartnn and sorry for disappearing i was using wrong aspects, which made me go nowhere. thanks again

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