The length of the perpendicular drawn from the origin to the plane 2x - 3y + 6z - 42 = 0 is: - Mathematics MCQ Mathematics Mock Test - 2 2026 | ExamTest.live

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The length of the perpendicular drawn from the origin to the plane 2 x - 3 y + 6 z - 42 = 0 is:

Solution & Step-by-step Explanation

The distance d of a point (x_{1}, y_{1}, z_{1}) from the plane a x + b y + cz + d = 0 is given by: D = \frac{∣ a x _{1} + b y _{1} + c z _{1} + d ∣}{a ^{2} + b ^{2} + c ^{2}} For the origin (0, 0, 0) and plane 2 x - 3 y + 6 z - 42 = 0 : D = \frac{∣2 ( 0 ) - 3 ( 0 ) + 6 ( 0 ) - 42∣}{2 ^{2} + ( - 3 ) ^{2} + 6 ^{2}} D = \frac{∣ - 42∣}{4 + 9 + 36} = \frac{42}{49} D = \frac{42}{7} = 6

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The length of the perpendicular drawn from the origin to the plane 2 x - 3 y + 6 z - 42 = 0 is:

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