Find the equation of the plane passing through the intersection of the planes \(x+2y+3z+4=0\) and \(4x+3y+2z+1=0\) and the origin.

Q.20 Find the equation of the plane passing through the intersection of the planes \(x+2y+3z+4=0\) and \(4x+3y+2z+1=0\) and the origin.

Doubtly Asked 29 Oct 2026 Board exam · July 2024 hsc 12th Save WhatsApp Report

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Answer: \(3x+2y+z=0\)

A plane through the line of intersection is \((x+2y+3z+4)+\lambda(4x+3y+2z+1)=0\).

It passes through \((0,0,0)\): \(4+\lambda=0\Rightarrow\lambda=-4\).

\((x+2y+3z+4)-4(4x+3y+2z+1)=0\Rightarrow-15x-10y-5z=0\Rightarrow3x+2y+z=0\).

Doubtly AI · 29 Oct 2026 AI-generated · not yet verified Report

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