Equation of line passing through  1,−1,0and parallel to the line having direction cosines 32,0,12  is

Equation of line passing through  $\left(1,-1,0\right)$and parallel to the line having direction cosines $〈\frac{\sqrt{3}}{2},0,\frac{1}{2}〉$  is

1. A

$\frac{x-\frac{\sqrt{3}}{2}}{1}=\frac{y-0}{-1}=\frac{z-\frac{1}{2}}{0}$

2. B

$\frac{x-1}{\sqrt{3}}=\frac{y+1}{0}=\frac{z}{1}$

3. C

$\frac{2x}{\sqrt{3}}=\frac{y}{0}=\frac{2z}{1}$

4. D

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

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Solution:

The equation of the line passing through the point  $\left({x}_{1},{y}_{1},{z}_{1}\right)$and parallel to the line whose direction ratios are$〈a,b,c〉$ is$\frac{x-{x}_{1}}{a}=\frac{y-{y}_{1}}{b}=\frac{z-{z}_{1}}{c}$

Here the direction cosines are $〈\frac{\sqrt{3}}{2},0,\frac{1}{2}〉$ , it implies that the direction ratios are$〈\sqrt{3},0,1〉$

Therefore, the equation of the line passing through the point $\left(1,-1,0\right)$and having direction ratios $〈\sqrt{3},0,1〉$ is  $\overline{)\frac{x-1}{\sqrt{3}}=\frac{y+1}{0}=\frac{z}{1}}$

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