Home
Class 12
MATHS
The OABC is a tetrahedron such that OA^2...

The OABC is a tetrahedron such that `OA^2+BC^2=OB^2+CA^2=OC^2+AB^2`,then

A

`OA bot BC`

B

`OB bot AC`

C

`OC bot AB`

D

`AB bot AC`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • PRODUCT OF VECTORS

    ARIHANT MATHS ENGLISH|Exercise JEE Type Solved Examples: Passage Based Type Questions|3 Videos

  • PRODUCT OF VECTORS

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 1|12 Videos

  • PROBABILITY

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|54 Videos

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|21 Videos

Similar Questions

Explore conceptually related problems

If G be the centroid of a triangle ABC, prove that, AB^2 + BC^2 + CA^2 = 3(GA^2 + GB^2 + GC^2)

In a tetrahedron OABC, the edges are of lengths, |OA|=|BC|=a,|OB|=|AC|=b,|OC|=|AB|=c. Let G_1 and G_2 be the centroids of the triangle ABC and AOC such that OG_1 _|_ BG_2, then the value of (a^2+c^2)/b^2 is

In an equilateral triangle ABC, BE is perpendicular to side CA. Prove that: AB^(2) + BC^(2) +CA^(2) = 4BE^(2)

OABC is a tetrahedron where O is the origin and A,B,C have position vectors veca,vecb,vecc respectively prove that circumcentre of tetrahedron OABC is (a^2(vecbxxvecc)+b^2(veccxxveca)+c^2(vecaxxvecb))/(2[veca vecb vecc])

In the triangle OAB , M is the midpoint of AB, C is a point on OM, such that 2 OC = CM . X is a point on the side OB such that OX = 2XB. The line XC is produced to meet OA in Y. Then (OY)/(YA)=

If AD, BE and CF are the medians of a Delta ABC, then evaluate (AD^(2)+BE^(2)+CF^(2)): (BC^(2) +CA^(2) +AB^(2)).

If OAB is a tetrahedron with edges and hatp, hatq, hatr are unit vectors along bisectors of vec(OA), vec(OB):vec(OB), vec(OC):vec(OC), vec(OA) respectively and hata=(vec(OA))/(|vec(OA)|), vecb=(vec(OB))/(|vec(OB)|), vec c= (vec(OC))/(|vec(OC)|) , then :

Diagonals of rhombus ABCD intersect each other at point O. Prove that : " "OA^(2)+OC^(2)=2AD^(2)-(BD^(2))/2

The point O is outside the angleABC . Show that 2(OA+OB+OC) gt AB+BC+CA .

A(1, -2) and B(2, 5) are two points. The lines OA, OB are produced to C and D respectively, such that OC=2OA and OD=2OB . Find CD .

ARIHANT MATHS ENGLISH-PRODUCT OF VECTORS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. The OABC is a tetrahedron such that OA^2+BC^2=OB^2+CA^2=OC^2+AB^2,then

    Text Solution

    |

  2. Let O be the origin and let PQR be an arbitrary triangle. The point S ...

    Text Solution

    |

  3. Let O be the origin and vec(OX) , vec(OY) , vec(OZ) be three unit vec...

    Text Solution

    |

  4. Let O be the origin, and O X , O Y , O Z be three unit vectors ...

    Text Solution

    |

  5. Let a, b and c be three unit vectors such that atimes(btimesc)=(sqrt(3...

    Text Solution

    |

  6. Let vec a , vec b and vec c be three non-zero vectors such that no ...

    Text Solution

    |

  7. If vec a , vec ba n d vec c are unit vectors satisfying | vec a- v...

    Text Solution

    |

  8. The vector(s) which is/are coplanar with vectors hat i+ hat j+2 hat...

    Text Solution

    |

  9. Let vec a= hat i+ hat j+ hat k , vec b= hat i- hat j+ hat ka n d vec ...

    Text Solution

    |

  10. Two adjacent sides of a parallelogram A B C D are given by vec A B=...

    Text Solution

    |

  11. Let P,Q R and S be the points on the plane with position vectors -2hat...

    Text Solution

    |

  12. If aa n db are vectors in space given by vec a=( hat i-2 hat j)/(sq...

    Text Solution

    |

  13. If veca,vecb,vecc and vecd are unit vectors such that (vecaxxvecb)*(...

    Text Solution

    |

  14. The edges of a parallelopiped are of unit length and are parallel to ...

    Text Solution

    |

  15. Let two non-collinear unit vectors veca and vecb form an acute angle. ...

    Text Solution

    |

  16. Let the vectors PQ,OR,RS,ST,TU and UP represent the sides of a regular...

    Text Solution

    |

  17. The number of distinct real values of lambda , for which the vectors...

    Text Solution

    |

  18. Let veca,vecb,vecc be unit vectors such that veca+vecb+vecc=vec0. Whic...

    Text Solution

    |

  19. Let vec A be a vector parallel to the line of intersection of plan...

    Text Solution

    |

  20. Let vec a= hat i+2 hat j+ hat k , vec b= hat i- hat j+ hat ka n d vec...

    Text Solution

    |

  21. The unit vector which is orthogonal to the vector 3hati+2hatj+6hatk an...

    Text Solution

    |