Home
Class 12
MATHS
Let A B C D be a tetrahedron such that ...

Let `A B C D` be a tetrahedron such that the edges `A B ,A C` and `A D` are mutually perpendicular. Let the area of triangles `A B C ,A C D` and `A D B` be `3, 4` and `5sq`. `units`, respectively. Then the area of triangle `B C D` is
a.`5sqrt(2)`
b. `5`
c. `(sqrt(5))/2`
d. `5/2`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS

    CENGAGE ENGLISH|Exercise Multiple Correct Answers Type|6 Videos
  • VECTORS TRIPLE PRODUCTS, RECIPROCAL SYSTEM OF VECTORS

    CENGAGE ENGLISH|Exercise DPP 2.4|20 Videos

Similar Questions

Explore conceptually related problems

Let A B C D be a tetrahedron such that the edges A B ,A Ca n dA D are mutually perpendicular. Let the area of triangles A B C ,A C Da n dA D B be 3, 4 and 5sq. units, respectively. Then the area of triangle B C D is a. 5sqrt(2) b. 5 c. (sqrt(5))/2 d. 5/2

A B C and B D E are two equilateral triangles such that D is the mid-point of B C . The ratio of the areas of the triangles A B C and B D E is 2:1 (b) 1:2 (c) 4:1 (d) 1:4

The equation of perpendicular bisectors of the side AB and AC of a triangle ABC are x-y+5=0 and x+2y=0 respectively vertex A is (1,-2) Area of triangle A B C is (in sq. units) (A) (36)/5 (B) (18)/5 (C) (72)/5 (D) None of these

The perpendicular A D on the base B C of a triangle A B C intersects B C at D so that D B=3C D . Prove that 2\ A B^2=2\ A C^2+B C^2 .

In an isosceles triangle A B C with A B=A C , B D is perpendicular from B to the side A C . Prove that B D^2-C D^2=2\ C D A D

In A B C , A D is perpendicular to B C . Prove that: A B^2+C D^2=A C^2+B D^2 (ii) A B^2-B D^2=A C^2-C D^2

In a triangle A B C ,\ \ A D_|_B C and A D^2=B DxxC Ddot Prove that A B C is a right triangle.

The diagonals of quadrilateral A B C D ,\ A C\ a n d\ B D intersect in O . Prove that if B O=O D , the triangles A B C\ a n d\ A D C are equal in area.

In Fig. , the area of A B C (in square units) is (a) 15 (b) 10 (c) 7.5 (d) 2.5

If the plane x/2+y/3+z/6=1 cuts the axes of coordinates at points, A ,B, and C , then find the area of the triangle A B C . a. 18 sq unit b. 36 sq unit c. 3sqrt(14) sq unit d. 2sqrt(14) sq unit

CENGAGE ENGLISH-VECTOR ALGEBRA-All Questions
  1. Let vec a=2 hati+hat j+ hat k , vec b=hat i+2hat j- hatk and a unit v...

    Text Solution

    |

  2. Let vec a=2i+j-2ka n d vec b=i+jdot If vec c is a vector such that ...

    Text Solution

    |

  3. Let A B C D be a tetrahedron such that the edges A B ,A C and A D ar...

    Text Solution

    |

  4. Vector vec a in the plane of vec b=2 hat i+ hat ja n d vec c= hat i...

    Text Solution

    |

  5. If vec a , vec b and vec c are non-coplanar unit vectors such that ...

    Text Solution

    |

  6. Let vec u , vec v and vec w be vectors such that vec u+ vec v+ vec w...

    Text Solution

    |

  7. If vec a , vec b and vec c are three non-coplanar vectors, then ( v...

    Text Solution

    |

  8. Let vec pa n d vec q be any two orthogonal vectors of equal magnitu...

    Text Solution

    |

  9. Let vec a , vec ba n d vec c be three non-coplanar vecrors and ve...

    Text Solution

    |

  10. Find a unit vector perpendicular to each of the vectors ( vec a+ vec...

    Text Solution

    |

  11. Consider three vectors vec a , vec b and vec c Statement 1 vec axx...

    Text Solution

    |

  12. Column I, Column II The possible value of vec a if vec r=( hat i+ ha...

    Text Solution

    |

  13. If vec A, vec B and vec C are vectors such that |vec B|-|vec C|. Prove...

    Text Solution

    |

  14. A parallelogram is constructed on 3 vec a+ vec ba n d vec a-4 vec b...

    Text Solution

    |

  15. Statement 1: Vector vec c=-5 hat i+7 hat j+2 hat k is along the bisec...

    Text Solution

    |

  16. Statement 1: A component of vector vec b=4 hat i+2 hat j+3 hat k in...

    Text Solution

    |

  17. Statement 1 : Points A(1,0),B(2,3),C(5,3),a n dD(6,0) are concyclic. S...

    Text Solution

    |

  18. Let vec r be a non-zero vector satisfying vec r dot vec a= vec rdo...

    Text Solution

    |

  19. Let vec a = a1 hat i + a2 hat j+ a3 hat k;vec b = b1 hat i+ b2 hat j+...

    Text Solution

    |

  20. Statement-I A=2hat(i)+3hat(j)+6hat(k), B=hat(i)+hat(j)-2hat(k) and C=h...

    Text Solution

    |