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Question

(A) The equation of a line passing through two points $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ is given by $\frac{x - x_1}{x_2 - x_1} = \frac{y - y_1}{

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$\frac{x - 4}{1} = \frac{y + 5}{-2} = \frac{z + 2}{-1}$

Vedclass · Answer

(A) The equation of a line passing through two points $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ is given by $\frac{x - x_1}{x_2 - x_1} = \frac{y - y_1}{y_2 - y_1} = \frac{z - z_1}{z_2 - z_1}$.Given points are $(x_1, y_1, z_1) = (4, -5, -2)$ and $(x_2, y_2, z_2) = (-1, 5, 3)$.Substituting these values into the formula:$\frac{x - 4}{-1 - 4} = \frac{y - (-5)}{5 - (-5)} = \frac{z - (-2)}{3 - (-2)}$Simplifying the denominators:$\frac{x - 4}{-5} = \frac{y + 5}{10} = \frac{z + 2}{5}$Dividing the denominators by $-5$:$\frac{x - 4}{1} = \frac{y + 5}{-2} = \frac{z + 2}{-1}$.Thus,the correct option is $A$.

The equation of the straight line passing through the points $(4, -5, -2)$ and $(-1, 5, 3)$ is

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