Plane P₃ is passing through (1,1,1) and line of intersection of P₁ and P₂ where \(P_{1}: 2x - y + z = 5\) and \(P_{2}: x + 3y + 2z + 2 = 0\). Then distance of (1,1,10) from P₃ is:

Updated On: Sep 09, 2024

\(\frac{53}{85}\)
\(\sqrt{85}\)
\(\frac{52}{\sqrt{85}}\)
53

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The Correct Option is C

Solution and Explanation

The correct option is (C): \(\frac{52}{\sqrt{85}}\)

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The correct option is

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Distance of a Point from a Plane

The shortest perpendicular distance from the point to the given plane is the distance between point and plane. In simple terms, the shortest distance from a point to a plane is the length of the perpendicular parallel to the normal vector dropped from the particular point to the particular plane. Let's see the formula for the distance between point and plane.