First slide

Straight lines in 3D

Question

$Equation of a line through (5,3,6) and parallel to z - axis is$

Easy

A

$\frac{x - 5}{0} = \frac{y - 3}{1} = \frac{z - 6}{0}$
B

$\frac{x - 5}{0} = \frac{y - 3}{0} = \frac{z - 6}{1}$
C

$\frac{x - 5}{1} = \frac{y - 3}{2} = \frac{z - 6}{5}$
D

$\frac{x - 5}{1} = \frac{y - 3}{0} = \frac{z - 6}{0}$

Solution

The direction cosines of $z -$ axis is $⟨ 0, 0, 1 ⟩$
The equation of the line passing through the point $(5, 3, 6)$ and having direction cosines $⟨ 0, 0, 1 ⟩$ is $\frac{x - 5}{0} = \frac{y - 3}{0} = \frac{z - 6}{1}$

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