Home
Class 12
MATHS
Let vec a , vec b , vec c are three non...

Let ` vec a , vec b , vec c` are three non-zero vectors such that ` vec axx vec b= vec ca n d vec bxx vec c= vec a ;` prove that ` vec a , vec b , vec c` are mutually at righ angles such that `| vec b|=1a n d| vec c|=| vec a|dot`

Promotional Banner

Topper's Solved these Questions

  • PRODUCT OF VECTORS

    ARIHANT MATHS|Exercise JEE Type Solved Examples: Passage Based Type Questions|3 Videos
  • PRODUCT OF VECTORS

    ARIHANT MATHS|Exercise JEE Type Solved Examples: Match Type Questions|4 Videos
  • PROBABILITY

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|55 Videos
  • PROPERTIES AND SOLUTION OF TRIANGLES

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

Similar Questions

Explore conceptually related problems

If vec a , vec b and vec c are three proper vectors such that vec a * vec b=vec c , vec b*vec c=vec a . Prove that vec a , vec b , vec c are mutually at right angles and |quad vec b|=1 ,|quad vec c|=|quad vec a|.

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| .

Prove that [vec a -vec b, vec b - vec c, vec c- vec a] =0

If vec a , vec b , vec c are vectors such that vec adot vec b= vec adot vec c , vec axx vec b= vec axx vec c , vec a!= vec0, then show that vec b= vec c

If vec a,vec b,vec c are any three vectors, prove that vec a xx (vec b xx vec c) +vec b xx(vec c xx vec a)+ vec c xx(vec a xx vec b) = vec 0

If vec a , vec b , vec c are three non-coplanar vectors and vec d* vec a = vec d* vec b= vec d* vec c= 0 then show that vec d is zero vector.

If vec a,vec b,vec c are three vectors such that vec a=vec b+vec c and the angle between vec b and vec c is pi/2, then

Prove that [vec a+ vec b, vec b +vec c, vec c + vec a]= 2 [vec a vec b vec c]

If vec a, vec b, vec c are unit vectors such that vec a+ vec b+ vec c = vec 0 , then find the value of vec a* vecb + vec b* vec c +vec c* veca .

If vec aa n d vec b are two vectors such that | vec axx vec b|=2, then find the value of [ vec a vec b vec axx vec b]dot

ARIHANT MATHS-PRODUCT OF VECTORS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let vec a , vec b , vec c are three non-zero vectors such that vec a...

    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. If veca, vecb, vecc are unit vectors such that veca+vecb+vecc=0, find...

    Text Solution

    |

  19. Let A be vector parallel to line of intersection of planes P1 and P2. ...

    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. Find the 7th term of GP if the first term is 7 and common ratio is 2.

    Text Solution

    |