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JEE Main 202324 JanuaryMorning Shift
Exam
JEE Main
Year
2023
Date
24 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Three Dimensional Geometry

JEE Main 2023 · 24 January · Morning Shift · Mathematics · Three Dimensional Geometry

The distance of the point (7, - 3, - 4) from the plane containing...

The distance of the point (7,−3,−4)\left(7, - 3, - 4\right) from the plane containing the points \left(2, - 3, 1\right), \left(- 1, 1, - 2\right) and \left(3, - 4, 2\right) is equal to:

Options

  1. A44
  2. B55
  3. C525\sqrt{2}
  4. D424\sqrt{2}

Correct answer

C. 525\sqrt{2}

Step-by-step solution

Equation of plane passing through the points (2,−3,1),(−1,1,−2)\left(2, - 3, 1\right), \left(- 1, 1, - 2\right) and \left(3, - 4, 2\right)is </p><p>\left|\begin{cases}x - 2 & y + 3 & z - 1 \\ - 3 & 4 & - 3 \\ 1 & - 1 & 1\end{cases}\right| = 0

⇒x−2−z+1=0⇒ x - 2 - z + 1 = 0

⇒x−z−1=0⇒ x - z - 1 = 0

Required distance is

=7+4−12= \dfrac{7 + 4 - 1}{\sqrt{2}}

= \dfrac{10}{\sqrt{2}} = 5\sqrt{2} units

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