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According to the Law of mathematics, the product of slopes of $2$ perpendicular lines has to be $ -1 $.

Then, how do you prove that the following lines are perpendicular.

$x=4$ , $y=6 $

Perpendicular lines

My Calculation :

Slope of line $1$ ($x=4$) = Infinity

Slope of line $2$ ($y=6$) = $0$

Product of both slopes != $0$

ILoveMath
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Karthik VU
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1 Answers1

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write them in vector notation, the horizontal line is spanned by the vector $ ( x, 0)$ and the vertical line is spanned by the vector $(0,y)$ Now we apply dot product

$$ (x,0) * (0,y) = x0 + 0y = 0 \implies \; \; \text{Both lines are orthogonal by definition} $$

ILoveMath
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