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:
- \(\frac{53}{85}\)
\(\sqrt{85}\)
- \(\frac{52}{\sqrt{85}}\)
- 53
The Correct Option is C
Solution and Explanation
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Concepts Used:
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.
Read More: Distance Between Two Points