Find the vector equation of the line passing through the point having position vector \(4\hat{i} - \hat{j} + 2\hat{k}\) and parallel to the vector \(-2\hat{i} - \hat{j} + \hat{k}\).

Q.8 Find the vector equation of the line passing through the point having position vector \(4\hat{i} - \hat{j} + 2\hat{k}\) and parallel to the vector \(-2\hat{i} - \hat{j} + \hat{k}\).

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

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Answer: \(\bar{r} = (4\hat{i} - \hat{j} + 2\hat{k}) + \lambda(-2\hat{i} - \hat{j} + \hat{k})\)

The vector equation of the line through \(A(\bar{a})\) parallel to \(\bar{b}\) is \(\bar{r} = \bar{a} + \lambda\bar{b}\), where \(\lambda\) is a scalar. Here \(\bar{a} = 4\hat{i} - \hat{j} + 2\hat{k}\) and \(\bar{b} = -2\hat{i} - \hat{j} + \hat{k}\), which gives the equation above.

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

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Find the vector equation of the line passing through the point having position vector \(4\hat{i} - \hat{j} + 2\hat{k}\) and parallel to the vector \(-2\hat{i} - \hat{j} + \hat{k}\).

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