Home
Class 12
MATHS
If vec a+ vec b+ vec c = vec 0 then prov...

If `vec a+ vec b+ vec c = vec 0` then prove that `vec axx vec b= vec bxx vec c = vec cxxvec a`.

Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

If 2vec a+ 3vecb + vec c = vec 0 , then show that vec axxvec b+vec bxxvec c+vec cxxvec a= 3(vec bxxvec c) .

Let vec a , vec b ,a n d vec c be non-coplanar vectors and let the equation vec a^' , vec b^' , vec c ' are reciprocal system of vector vec a , vec b , vec c , then prove that vec axx vec a^'+ vec bxx vec b^'+ vec cxx vec c ' is a null vector.

Let vec a , vec b ,and vec c be any three vectors, then prove that [ vec axx vec b vec bxx vec c vec cxx vec a ]= [vec a vec b vec c]^2

If vec a , vec b , and vec c are three vectors such that vec axx vec b= vec c , vec bxx vec c= vec a , vec cxx vec a= vec b , then prove that | vec a|=| vec b|=| vec c| .

For any four vectors, vec a , vec b , vec c and vec d prove that vec d.( vec axx( vec bxx( vec cxx vec d)))=( vec b. vec d)[ vec a \ vec c \ vec d] .

If vec a+2 vec b+3 vec c=0,t h e n vec axx vec b+ vec bxx vec c+ vec cxx vec a= a. 2( vec axx vec b) b. 6( vec bxx vec c) c. 3( vec cxx vec a) d. vec0

If 4 vec a+5 vec b+9 vec c=0, then ( vec axx vec b)xx[( vec bxx vec c)xx( vec cxx vec a)] is equal to a. vector perpendicular to the plane of a ,b ,c b. a scalar quantity c. vec0 d. none of these

If vec a and vec b are two vectors, then prove that ( vec axx vec b)^2=|[vec a.vec a,vec a.vec b],[vec b.vec a,vec b.vec b]| .

The lines vec r= vec a+lambda( vec bxx vec c)a n d vec r= vec b+mu( vec cxx vec a) will intersect if a. vec axx vec c= vec bxx vec c b. vec adot vec c= vec bdot vec c c. bxx vec a= vec cxx vec a d. none of these

If vec a, vec b, vec c are unit vectors satisfying the condition veca+ vec b+ vec c= 0 then show that vec a. vec b+ vec b.vec c+ vec c. vec a= -3//2 .

UNITED BOOK HOUSE-SET 6-EXERCISE
  1. Solve: (1+x^2)(dy)/(dx) = y+tan^(-1)x

    Text Solution

    |

  2. If vec p is a unit vector and (vec x- vecp).(vec x+ vecp) = 8 then fin...

    Text Solution

    |

  3. Find the intercepts made by the plane x-2y+3z-18=0 on the axes.

    Text Solution

    |

  4. If P(A) = 5/13,P(B)= 6/13 and P(AuuB) = 7//13 then find P(bar A//B) a...

    Text Solution

    |

  5. The mean and variance of a binomial distribution are 16 and 12 respect...

    Text Solution

    |

  6. Prove that tan^(-1) {(sqrt(1+cos x)+sqrt(1-cosx))/(sqrt(1+cos x)-sqrt(...

    Text Solution

    |

  7. Let A = [[1,0],[-1,7]] and I = [[1,0],[0,1]] then find the K when A^2=...

    Text Solution

    |

  8. Show that A = [[1,2,2],[2,1,2],[2,2,1]] satrisfies the matrix equation...

    Text Solution

    |

  9. If alpha,beta,gamma are in A.P. then show that , |[x-3,x-4,x-alpha],[x...

    Text Solution

    |

  10. If sqrt(1-x^6)+sqrt(1-y^6) = a(x^3-y^3) then prove that (dy)/(dx)= x^2...

    Text Solution

    |

  11. If y = (x+ sqrt(1+x^2))^n then prove that (1+x^2)y2+xy1 = n^2y.

    Text Solution

    |

  12. Evaluate: int (dx)/(1+tanx)

    Text Solution

    |

  13. Evaluate: int e^x (2-sin 2x)/(1-cos 2x)dx

    Text Solution

    |

  14. Solve: (x+3)(dy)/(dx)-3y =(x+3)^5

    Text Solution

    |

  15. Solve: y^2dx+(xy+x^2)dy =0

    Text Solution

    |

  16. If vec axx vec b= vec cxxvec d and vec axxvec c= vec bxxvec d, vec a n...

    Text Solution

    |

  17. A and B toss a coin alternately untill one of them gets a head for the...

    Text Solution

    |

  18. Show that the sum of the intercepts of the tangent to the curve sqrtx+...

    Text Solution

    |

  19. Prove that the perpendicular distance of the line 3x+4y+5 =0 from ori...

    Text Solution

    |

  20. If vec a+ vec b+ vec c = vec 0 then prove that vec axx vec b= vec bxx ...

    Text Solution

    |