First slide

Straight lines in 3D

Question

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

Very Easy

A

$\frac{x - 2}{1} = \frac{y - 3}{5} = \frac{z + 1}{- 4}$
B

$\frac{x - 2}{- 1} = \frac{y - 3}{- 5} = \frac{z + 5}{- 4}$
C

$\frac{x + 2}{1} = \frac{y + 3}{5} = \frac{z + 5}{4}$
D

$\frac{x - 2}{1} = \frac{y - 3}{5} = \frac{z - 5}{4}$

Solution

Equation of a line passing through the points $A (x_{1}, y_{1}, z_{1})$ and $B (x_{2}, y_{2}, z_{2})$ 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 passing through the points $(2, 3, 5), (1, - 2, 1)$ is $\frac{x - 2}{1} = \frac{y - 3}{5} = \frac{z - 5}{4}$

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