First slide

Straight lines in 3D

Question

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

Very Easy

A

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

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

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

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

Solution

The given points are $(- 2, 4, 2)$ and $(7, - 2, 5)$
The direction ratios are $<9, - 6, 3> = <3, - 2, 1>$
The equation of the line joining the points $A (x_{1}, y_{1}, z_{1}), B (x_{2}, y_{2}, z_{2})$ 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 $(- 2, 4, 2)$ and $(7, - 2, 5)$ is $\frac{x + 2}{3} = \frac{y - 4}{- 2} = \frac{z - 2}{1}$

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