Find the vector equation of the plane passing through the point having position vector \(2\hat i + 3\hat j + 4\hat k\) and perpendicular to the vector \(2\hat i + \hat j - 2\hat k\).

Q.8 Find the vector equation of the plane passing through the point having position vector \(2\hat i + 3\hat j + 4\hat k\) and perpendicular to the vector \(2\hat i + \hat j - 2\hat k\).

Doubtly Asked 28 Oct 2026 Board exam · March 2025 hsc 12th Save WhatsApp Report

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Answer: \(\bar r\cdot(2\hat i + \hat j - 2\hat k) = -1\)

The plane through \(A(\bar a)\) perpendicular to \(\bar n\) is \(\bar r\cdot\bar n = \bar a\cdot\bar n\).

\(\bar a\cdot\bar n = (2)(2) + (3)(1) + (4)(-2) = 4 + 3 - 8 = -1\).

Hence \(\bar r\cdot(2\hat i + \hat j - 2\hat k) = -1\).

Doubtly AI · 28 Oct 2026 AI-verified · Oct 2026 Report

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Find the vector equation of the plane passing through the point having position vector \(2\hat i + 3\hat j + 4\hat k\) and perpendicular to the vector \(2\hat i + \hat j - 2\hat k\).

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