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Question
Find the vector equation of a plane which is at a distance of 5 units from the origin and its normal vector is \[2 \hat{i} - 3 \hat{j} + 6 \hat{k} \] .
Solution
Given:
\[\text{Normal vector } , \hat{n} = 2 \hat{i} - 3 \hat{j} + 6 \hat{k} \]
\[\text{ Perpendicular distance, d = 5 units } \]
The vector equation of a plane that is at a distance of 5 units from the origin and has its normal vector \[\hat{n} = 2 \hat{i} - 3 \hat{j} + 6 \hat{k} \] is as follows:
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