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The Cartesian equation of the line passing through the points \(A(3, 4, -1)\) and \(B(2, -1, 3)\) is _____.

Q.1 (iv) The Cartesian equation of the line passing through the points \(A(3, 4, -1)\) and \(B(2, -1, 3)\) is _____.

A. \(\frac{x+3}{1} = \frac{y-4}{5} = \frac{z+1}{-4}\)

B. \(\frac{x-3}{-1} = \frac{y-4}{-5} = \frac{z+1}{-4}\)

C. \(\frac{x-3}{-1} = \frac{y-4}{-5} = \frac{z+1}{4}\)

D. \(\frac{x-3}{-1} = \frac{y-4}{5} = \frac{z+1}{-4}\)

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Best answer

Answer: C. \(\frac{x-3}{-1} = \frac{y-4}{-5} = \frac{z+1}{4}\)

Answer: (c) \(\frac{x-3}{-1} = \frac{y-4}{-5} = \frac{z+1}{4}\)

Direction ratios of AB: \(2-3,\ -1-4,\ 3-(-1)\), i.e. \(-1, -5, 4\). The line through \(A(3, 4, -1)\) is \(\frac{x-3}{-1} = \frac{y-4}{-5} = \frac{z+1}{4}\).

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