Kerala KEAM 5 June 2024 Solved Paper

The given equation of the line is in vector form: $$\overrightarrow{r} = \hat{i} + t \hat{j}, \quad t \in \mathbb{R}.$$This represents a line passing through the point $(1, 0, 0)$ with direction vector $(0, 1, 0)$. The symmetric form of a line equation is given by: $$\frac{x - x_1}{a} = \frac{y - y_1}{b} = \frac{z - z_1}{c},$$where $(x_1, y_1, z_1)$ is a point on the line and $(a, b, c)$ is the direction vector.For this case, the point on the line is $(1, 0, 0)$, and the direction vector is $(0, 1, 0)$. Thus, the symmetric form of the equation is: $$\frac{x - 1}{0} = \frac{y}{1} = \frac{z}{0}.$$Thus, the correct answer is option (A).Quick Tip: In the symmetric form of a line equation, the point on the line is represented as $(x_1, y_1, z_1)$, and the direction ratios are used in the denominators. If the direction vector has zero components, it will appear as a zero in the corresponding term.