First slide

Straight lines in 3D

Question

The symmetric form of the line $x = a y + b,$ and $z = c y + d$

Easy

A

$\frac{x - a}{b} = \frac{y}{1} = \frac{z - c}{d}$
B

$\frac{x - b}{a} = \frac{y}{1} = \frac{z - d}{c}$
C

$\frac{x + a}{b} = \frac{y}{1} = \frac{z - c}{d}$
D

$\frac{x - b}{a} = \frac{y}{1} = \frac{z + d}{c}$

Solution

The given equation is $x = a y + b,$ and $z = c y + d$
find the expression for $y$
it implies $y = \frac{x - b}{a}$ and $y = \frac{z - d}{c}$
Therefore, the equation of the line in symmetric form is $\frac{x - b}{a} = \frac{y}{1} = \frac{z - d}{c}$

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