What is the vector equation of a line passing through the point (1, 3, 4) and parallel to the vector i - j + 2k?

April 13, 2026Mathematics

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April 13, 2026

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Q1. The vector equation of a line passing through the point $(1, 3, 4)$ and parallel to the vector $\mathbf{i} - j + 2\mathbf{k}$ is given by the formula $\mathbf{r} = a + \lambda \mathbf{b}$ , where $\mathbf{a}$ is the position vector of the point and $\mathbf{b}$ is the direction vector. Step 1: Identify the position vector $\mathbf{a}$ and the direction vector $\mathbf{b}$ . The point is $(1, 3, 4)$ , so $\mathbf{a} = \mathbf{i

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Asked on April 13, 2026Mathematics

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ScanSolve AI AnswerAnswered on April 13, 2026

Hey nkemdivo — ready when you are. Here are the solutions to the questions: Q1. The vector equation of a line passing through the point (1, 3, 4) and parallel to the vector i - j + 2k is given by the formula r = a + b, where a is the position vector of the point and b is the direction vector. Step 1: Identify the position vector a and the direction vector b. The point is (1, 3, 4), so $a = i