Gọi `(d):ax+by-3=0`
`M(1;1)\in (d)`
`=>a.1+b.1-3=0`
`<=>b=3-a`
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`(∆):3x-y+7=0`
`\vec{n_d}=(a;b)`
`\vec{n_∆}=(3;-1)`
`=>cos(d;∆)=cos(\vec{n_d};\vec{n_∆})`
`<=>cos45°={|\vec{n_d}.\vec{n_∆}|}/{|\vec{n_d}|.|\vec{n_∆}|}`
`<=>\sqrt{2}/2={|3a-b|}/{\sqrt{a^2+b^2}.\sqrt{3^2+(-1)^2}`
`<=>\sqrt{2}/2={|3a-b|}/{sqrt{10(a^2+b^2)}`
`<=>2|3a-b|=\sqrt{20(a^2+b^2)}`
`<=>|3a-b|=\sqrt{5(a^2+b^2)}`
`<=>(3a-b)^2=5(a^2+b^2)`
`<=>[3a-(3-a)]^2=5[a^2+(3-a)^2]`
`<=>16a^2-24a+9=5(a^2+a^2-6a+9)`
`<=>6a^2+6a-36=0`
`<=>a^2+a-6=0`
$⇔\left[\begin{array}{l}a=2\\a=-3\end{array}\right.$$⇒\left[\begin{array}{l}b=3-a=3-2=1\\b=3-a=3+3=6\end{array}\right.$
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+) Với `a=2;b=1`
`=>a-b=2-1=1`
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+) Với `a=-3;b=6`
`=>a-b=-3-6=-9`
