Home
Class 12
MATHS
The position vector of the vertices A, B...

The position vector of the vertices A, B & C of a tetrahedron ABCD are (1, 1, 1), (1, 0, 0) & (3, 0, 0) respectively. The altitude from the vertex D to the opposite face ABC meets the median through A of ` A B C` at point E. If `A D=4` units and value of tetrahedron `=(2sqrt(2))/3,` then the correct statement(s) among the following is/are: The altitude from vertex `D=2` units There is only one possible position for point E There are two possible position for point E vector ` hat j- hat k` is normal to the plane ABC

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP ENGLISH|Exercise All Questions|15 Videos

  • MATRICES

    RESONANCE DPP ENGLISH|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

If the vertices A,B,C of a triangle ABC are (1,2,3),(-1,0,0) ,(0,1,2) , respectively, then find angleABC .

The position vectors of the vertices A, B and C of a tetrahedron ABCD are hat i + hat j + hat k , hat k , hat i and hat 3i ,respectively. The altitude from vertex D to the opposite face ABC meets the median line through Aof triangle ABC at a point E. If the length of the side AD is 4 and the volume of the tetrahedron is2√2/3, find the position vectors of the point E for all its possible positions

If the vectors A ,B ,C of a triangle A B C are (1,2,3),(-1,0,0),(0,1,2), respectively then find /_A B Cdot

If the three vertices of a parallelogram ABCD are A(3, -1, 5), B(1, -2, -4) and C(0, 3, 0), then the coordinates of fourth vertex is

The position vectors of the four angular points of a tetrahedron OABC are (0, 0, 0); (0, 0,2) , (0, 4,0) and (6, 0, 0) respectively. A point P inside the tetrahedron is at the same distance r from the four plane faces of the tetrahedron. Find the value of 3r

The position vectors of the four angular points of a tetrahedron OABC are (0, 0, 0); (0, 0,2) , (0, 4,0) and (6, 0, 0) respectively. A point P inside the tetrahedron is at the same distance r from the four plane faces of the tetrahedron. Find the value of r

The position vectors of the four angular points of a tetrahedron OABC are (0, 0, 0), (0, 0, 2), (0, 4, 0) and (6, 0, 0) , respectively. A point P inside the tetrahedron is at the same distance 'r' from the four plane faces of the tetrahedron. Then, the value of 9r is.....

Three vertices of a parallelogram ABCD are A(3, 1, 2), B(0, 1, 5) and C(-1, 2, -3) Find the coordinates of the fourth vertex.

The vertices of A B C are (-2,\ 1),\ (5,\ 4) and (2,\ -3) respectively. Find the area of the triangle and the length of the altitude through A .

In triangle ABC, the co-ordinates of vertices A, B and C are (4, 7), (-2, 3) and (0, 1) respectively. Find the equation of median through vertex A. Also, find the equation of the line through vertex B and parallel to AC.

RESONANCE DPP ENGLISH-JEE MAINS-All Questions
  1. Consider the following statements. p : Hari is clever. q: shyam is foo...

    Text Solution

    |

  2. Show that the area of the triangle formed by the lines y=m1x+c1,""...

    Text Solution

    |

  3. The position vector of the vertices A, B & C of a tetrahedron ABCD ...

    Text Solution

    |

  4. If the lines (x+4)/3=(y+6)/5=(z-1)/(-2) and 3x-2y+z+5=0=2x+3y+4z-k are...

    Text Solution

    |

  5. Let f(x)=cot^(-1)(x^2+4x+alpha^2-3alpha) be a function defined on R->(...

    Text Solution

    |

  6. A natural number x is chosen at random from the first one hundred natu...

    Text Solution

    |

  7. If the functions f(x)a n dg(x) are defined on RvecR such that f(x)={0,...

    Text Solution

    |

  8. If the fourth term in the expansion of {sqrt(1/("""x^log(x+1)"}'+1/(x^...

    Text Solution

    |

  9. If H is the othrocenter of an acute angled triangle ABC whose circumci...

    Text Solution

    |

  10. Let vec a=2 hat i-3 hat j, vec b= hat i+ hat j- hat k and hat c=3 ha...

    Text Solution

    |

  11. The chord of contact of a point P w.r.t a hyperbola and its auxiliary ...

    Text Solution

    |

  12. Distance between line r=i+j+k+lambda(2i+j+4k) and plane rdot(i+2j-k)=3...

    Text Solution

    |

  13. An endless inextensible string of length 15 m passes around two pins, ...

    Text Solution

    |

  14. The direction cosines of the lines bisecting the angle between the lin...

    Text Solution

    |

  15. If f(x) is identity function, g(x) is absolute value function and h(...

    Text Solution

    |

  16. Consider two curves C1: y^2=4[sqrt(y)]x a n dC2: x^2=4[sqrt(x)]y , whe...

    Text Solution

    |

  17. In a DeltaABC if /A=/B=1/2(sin^(-1)((sqrt(6)+1)/(2sqrt(3)))+sin^(-1)(...

    Text Solution

    |

  18. The distance of the point (1, 2, 3) from the plane x+y-z=5 measured al...

    Text Solution

    |

  19. if alpha, beta, gamma are the roots of equation x^3-x-1=0 , then (1+...

    Text Solution

    |

  20. Let f(x) be a non constant twice differentiable function defined on (-...

    Text Solution

    |