The equation of the line joining the points   −2,4,2and 7,−2,5 is

# The equation of the line joining the points   $\left(-2,4,2\right)$and $\left(7,-2,5\right)$ is

1. A

$\frac{x+2}{3}=\frac{y-4}{-2}=\frac{z-1}{1}$

2. B

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

3. C

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

4. D

$\frac{x+2}{5}=\frac{y-4}{2}=\frac{z-1}{7}$

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### Solution:

The given points are   $\left(-2,4,2\right)$and  $\left(7,-2,5\right)$

The direction ratios are

The equation of the line joining the points$A\left({x}_{1},{y}_{1},{z}_{1}\right),B\left({x}_{2},{y}_{2},{z}_{2}\right)$  is$\frac{x-{x}_{1}}{{x}_{2}-{x}_{1}}=\frac{y-{y}_{1}}{{y}_{2}-{y}_{1}}=\frac{z-{z}_{1}}{{z}_{2}-{z}_{1}}$

Therefore, the equation of the line joining the points  $\left(-2,4,2\right)$and  $\left(7,-2,5\right)$is  $\overline{)\frac{x+2}{3}=\frac{y-4}{-2}=\frac{z-2}{1}}$

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