Question
Find the Cartesian equations of the line which passes through the point (-2, 4, -5) and

parallel to the line $\frac{x+2}{3}=\frac{y-3}{5}=\frac{z+5}{6}$

Answer

The line $\frac{x+2}{3}=\frac{y-3}{5}=\frac{z+5}{6}$ has direction ratios $3,5,6$. The required line has direction

ratios 3, 5, 6 as it is parallel to the given line. It passes through the point (-2, 4, -5). The cartesian equations of the line passing through (x1, y1, z1) and having direction ratios a, b, c are

$\frac{x-x_1}{a}=\frac{y-y_1}{b}=\frac{2-z_1}{c}$

$\therefore$ the required cartesian equations of the line are

$\frac{x-(-2)}{3}=\frac{y-4}{5}=\frac{z-(-5)}{6}$

i.e. $\frac{x+2}{3}=\frac{y-4}{5}=\frac{z+5}{6}$

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