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Three Dimensional Geometry — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsThree Dimensional Geometry1 Mark
Question
Write the vector equation of the plane, passing through the point (a, b, c) and parallel to the plane $\overrightarrow{\text{r}}.(\hat{\text{i}} + \hat{\text{j}} + \hat{\text{k}}) = 2.$
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Answer

$\left\{\overrightarrow{\text{r}} - \big(\text{a}\hat{\text{i}} + \text{b}\hat{\text{j}} + \text{c}\hat{\text{k}}\big)\right\}.\big(\hat{\text{i}} + \hat{\text{j}} +\hat{\text{k}}\big) = 0$
Alternate Answer
$\overrightarrow{\text{r}}\cdot\big(\hat{\text{i}} + \hat{\text{j}} +\hat{\text{k}}\big) =\text{a } + \text{b } +\text{c}.$

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