Home
Class 12
MATHS
Given three non-coplanar vectors OA=a, O...

Given three non-coplanar vectors OA=a, OB=b, OC=c. Let S be the centre of the sphere passing through the points O, A, B, C if OS=x, then

A

x must be linear combination of a, b, c

B

x must be linear combination of `btimesc, ctimesa and atimesb`

C

`x=(a^(2)(btimesc)+b^(2)(ctimesa)+c^(2)(atimesb))/(2[a b c]), a=|a|, b=|b|. C=|c|`

D

`x=a+b+c`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
Promotional Banner

Topper's Solved these Questions

  • PRODUCT OF VECTORS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Statement I And Ii Type Questions)|12 Videos

  • PRODUCT OF VECTORS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Passage Based Questions)|21 Videos

  • PRODUCT OF VECTORS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Single Option Correct Type Questions)|71 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

Find the vector equation of a plane passing through three points A(0, 0, 2), B(1, -1, 1), C(3, 4, 5) .

The centre of circle passing through three non collinear points A,B,C is the concurrent point of

A line is at a distance c from origin and meets axes in A and B. The locus of the centre of the circle passing through O,A,B is

A line is at a distance 'c' from origin and meets axes in A and B. The locus of the centre of the circle passing through O,A,B is

Statement 1: there exists a unique sphere which passes through the three non-collinear points and which has the least radius. Statement 2: The centre of such a sphere lies on the plane determined by the given three points.

Statement 1: there exists a unique sphere which passes through the three non-collinear points and which has the least radius. Statement 2: The centre of such a sphere lies on the plane determined by the given three points.

veca , vec b , vec c are non-coplanar vectors and x vec a + y vec b + z vec c = vec 0 then

If O A B C is a tetrahedron where O is the orogin anf A ,B ,a n dC are the other three vertices with position vectors, vec a , vec b ,a n d vec c respectively, then prove that the centre of the sphere circumscribing the tetrahedron is given by position vector (a^2( vec bxx vec c)+b^2( vec cxx vec a)+c^2( vec axx vec b))/(2[ vec a vec b vec c]) .

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

If a plane cuts off intercepts OA = a, OB = b, OC = c from the coordinate axes 9where 'O' is the origin). then the area of the triangle ABC is equal to

ARIHANT MATHS ENGLISH-PRODUCT OF VECTORS-Exercise (More Than One Correct Option Type Questions)
  1. Let a, b and c be non-zero vectors and |a|=1 and r is a non-zero vecto...

    Text Solution

    |

  2. If veca and vecb are two unit vectors perpendicular to each other and...

    Text Solution

    |

  3. Given three non-coplanar vectors OA=a, OB=b, OC=c. Let S be the centre...

    Text Solution

    |

  4. If a=hat(i)+hat(j)+hat(k) and b=hat(i)-hat(j), then the vectors (a*hat...

    Text Solution

    |

  5. If vec a=x hat i+y hat j+z hat k , vec b=y hat i+z hat j+x hat k and v...

    Text Solution

    |

  6. If veca, vecb, vecc are three non-zero vectors, then which of the foll...

    Text Solution

    |

  7. Unit vectors veca and vecb ar perpendicular , and unit vector vecc is ...

    Text Solution

    |

  8. If a, b, c are three non-zero vectors, then which of the following sta...

    Text Solution

    |

  9. Let veca and vecb be two non- zero perpendicular vectors. A vector vec...

    Text Solution

    |

  10. If veca and vecb are any two unit vectors, then find the greatest post...

    Text Solution

    |

  11. If a is perpendicular to b and p is non-zero scalar such that pr+(r*b)...

    Text Solution

    |

  12. In a four-dimensional space where unit vectors along the axes are h...

    Text Solution

    |

  13. A vector(d) is equally inclined to three vectors a=hat(i)-hat(j)+hat(k...

    Text Solution

    |

  14. If a, b, c are non-zero, non-collinear vectors such that a vectors suc...

    Text Solution

    |

  15. Given three vectors veca, vecb and vecc are non-zero and non-coplanar ...

    Text Solution

    |

  16. If r=hat(i)+hat(j)+lambda(2hat(i)+hat(j)+4hat(k)) and r*(hat(i)+2hat(j...

    Text Solution

    |

  17. If vectors veca and vecb are two adjecent sides of a paralleogram, the...

    Text Solution

    |

  18. Let a, b, c be three vectors such that each of them are non-collinear,...

    Text Solution

    |

  19. If a, b and c are non-collinear unit vectors also b, c are non-colline...

    Text Solution

    |

  20. If a=(1)/(7)(2hat(i)+3hat(j)+6hat(k)): b=(1)/(7)(6hat(i)+2hat(j)-3hat...

    Text Solution

    |