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Question
Find the length of the perpendicular drawn from the origin to the plane 2x − 3y + 6z + 21 = 0.
Solution
\[\text{ We know that the distance of the point } \left( x_1 , y_1 , z_1 \right) \text{ from the plane } ax + by + cz + d = 0 \text{ is given by} \]
\[\frac{\left| a x_1 + b y_1 + c z_1 + d \right|}{\sqrt{a^2 + b^2 + c^2}}\]
\[\text{ So, the required distance} \]
\[ = \frac{\left| 2 \left( 0 \right) - 3 \left( 0 \right) + 6 \left( 0 \right) + 21 \right|}{\sqrt{2^2 + \left( - 3 \right)^2 + 6^2}}\]
\[ = \frac{\left| 21 \right|}{\sqrt{4 + 9 + 36}}\]
\[ = \frac{21}{7}\]
\[ = 3 \text{ units} \]
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