Find the vector equation of the line passing through the points \(A(1, 2, 3)\) and \(B(2, 3, 4)\).
Q.8 Find the vector equation of the line passing through the points \(A(1, 2, 3)\) and \(B(2, 3, 4)\).
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Answer: \(\bar{r} = (\hat{i} + 2\hat{j} + 3\hat{k}) + \lambda(\hat{i} + \hat{j} + \hat{k})\)
\(\bar{a} = \hat{i} + 2\hat{j} + 3\hat{k}\), \(\bar{b} = 2\hat{i} + 3\hat{j} + 4\hat{k}\). The line through \(A\) and \(B\) is \(\bar{r} = \bar{a} + \lambda(\bar{b} - \bar{a})\), and \(\bar{b} - \bar{a} = \hat{i} + \hat{j} + \hat{k}\).
So \(\bar{r} = (\hat{i} + 2\hat{j} + 3\hat{k}) + \lambda(\hat{i} + \hat{j} + \hat{k})\), \(\lambda\) a scalar.
Doubtly AI
· 28 Oct 2026
AI-verified · Oct 2026
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