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## shahzadjalbani Group Title Why is the product of the gradients of 2 straight line perpendicular to each other is always equal to -1 ?? Please prove it......? 2 years ago 2 years ago

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1. shirleyx

m1=1/m2 you can use two rules (straight line) to prove it. |dw:1338626026029:dw|

2. shahzadjalbani

Give me a hint?

3. myko

you can write equation of the lines perpedicular to each other in this form: ax+by=0 -bx+ay=0 this is a hint....:)

4. shahzadjalbani

Can you prove it through trigonometry?

5. shahzadjalbani

@myko @shirleyx Can you prove it through trigonometry?

6. experimentX

slope = $$\tan(\theta)$$ another slope = $$\tan(\theta - 90) = -\cot \theta$$

7. myko

$\cos \alpha x+\sin \alpha y =0$ $-\sin \alpha x + \cos \alpha y =0$

8. myko

grad f1 = (cosa -sinax,sina+cosay) grad f2 = (-sina-cosax,cosa-sinay)