English, asked by kareenazehramody, 3 months ago


1) Derive the equation of a plane in a normal form (5 marks)

Answers

Answered by shashankhc58
21

ΛПƧЩΣЯ

Let L be the line whose perpendicular distance from origin is P, angle XOA =ѳ

Draw AM perpendicular to x-axis.

Then AM=Psinѳ, OM=Pcosѳ

Point A=(Pcosѳ Psinѳ)

Now slope of OA =tanѳ

OA is perpendicular to Line L.

slope \: of \: line \: l \:  =  \frac{ - 1}{ \tan(ѳ) }  \\ l =  \frac{ -  \cos(ѳ) }{ \sin(ѳ) }

Equation of line is

✈ y-y1=m(x-x1) [Point slope form]

y - p \sin(ѳ)  =  \frac{ -  \cos(ѳ) }{ \sin(ѳ) } (x -pcosѳ) \\ y \sin(ѳ) - p  {sin}^{2} ѳ =  - x \cos ѳ + p {cos}^{2} ѳ \\ x \cos(ѳ )  + y \sin(ѳ)  = p {cos}^{2} ѳ + p {sin}^{2} ѳ \\ x \cos(ѳ)  + y \sin(ѳ)  = p( {sin}^{2} ѳ +  {cos}^{2}ѳ  ) \\ x \cos(ѳ)  + y \sin(ѳ)  = p(1)

x \cos(ѳ)  + y \sin(ѳ)  = p

5 thanks ✈️

➡️ Fo I l o w me ⬅️

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