First slide

Straight lines in 3D

Question

The symmetric form of the line whose parametric equations are given by $x = 1 - 2 t, y = t, z = - 1 + t$ is

Easy

A

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

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

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

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

Solution

The parametric equation of the given line $x = 1 - 2 t, y = t, z = - 1 + t$
it gives $\frac{x - 1}{- 2} = t, \frac{y}{1} = t, \frac{z + 1}{1} = t$
Equation of the given line is $\frac{x - 1}{- 2} = \frac{y}{1} = \frac{z + 1}{1}$

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