First slide

Straight lines in 3D

Question

The equation of a line passing through the point on Z-axis at 2 units distance from origin having direction cosines $⟨ 0, 1, - 1 ⟩$ is

Moderate

A

$\frac{x}{1} = \frac{y}{0} = \frac{z}{2}$
B

$\frac{x}{1} = \frac{y + 1}{0} = \frac{z + 1}{1}$
C

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

$\frac{x}{0} = \frac{y}{1} = \frac{z - 2}{- 1}$

Solution

A point on Z-axis at 2 units distance from origin is $(0, 0, 2)$
The equation of the line passing through the point $(x_{1}, y_{1}, z_{1})$ and having direction cosines $⟨ l, m, n ⟩$ is $\frac{x - x_{1}}{l} = \frac{y - y_{1}}{m} = \frac{z - z_{1}}{n}$
Equation of line passing through $(0, 0, 2)$ and having direction cosines $⟨ 0, 1, - 1 ⟩$ is $\frac{x}{0} = \frac{y}{1} = \frac{z - 2}{- 1}$

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