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JEE Main 20252 AprilMorning Shift
Exam
JEE Main
Year
2025
Date
2 April
Shift
Morning Shift
Subject
Mathematics
Chapter
Vector Algebra

JEE Main 2025 · 2 April · Morning Shift · Mathematics · Vector Algebra

Let A B C D be a tetrahedron such that the edges AB, AC and AD are...

Let ABCDA B C D be a tetrahedron such that the edges AB,AC\mathrm{AB}, \mathrm{AC} and AD are mutually perpendicular. Let the areas of the triangles ABC,ACD\mathrm{ABC}, \mathrm{ACD} and ADB be 5,6 and 7 square units respectively. Then the area (in square units) of the △BCD\triangle \mathrm{BCD} is equal to :

Options

  1. A340\sqrt{340}
  2. B12
  3. C110\sqrt{110}
  4. D737 \sqrt{3}

Correct answer

C. 110\sqrt{110}

Step-by-step solution

Ar⁡(△BCD)\operatorname{Ar}(\triangle B C D)
=(Ar⁡(△ABC))2+(Ar(ACD))2+(Ar⁡(△ADB))2=\sqrt{(\operatorname{Ar}(\triangle \mathrm{ABC}))^2+(\mathrm{Ar}(\mathrm{ACD}))^2+(\operatorname{Ar}(\triangle \mathrm{ADB}))^2}
=52+62+72=\sqrt{5^2+6^2+7^2}
=110=\sqrt{110}
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