Home
Class 12
MATHS
If veca and vecb are two unit vectors p...

If `veca and vecb ` are two unit vectors perpendicular to each other and `vecc=lamda_1veca+lamda_2vecb+lamda_3(vecaxxvecb)` then the following is (are) true

A

(a)`lambda_1=a*c`

B

(b)`lambda_2=|atimesb|`

C

(c)`lambda_3=|(atimesb)timesc|`

D

(d)`lambda_1+lambda_2+lambda_3=(a+b+atimesb)*c`

Text Solution

Verified by Experts

The correct Answer is:
A, D
Promotional Banner

Topper's Solved these Questions

  • PRODUCT OF VECTORS

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

  • PRODUCT OF VECTORS

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

  • PRODUCT OF VECTORS

    ARIHANT MATHS|Exercise Exercise (Single Option Correct Type Questions)|71 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
ARIHANT MATHS-PRODUCT OF VECTORS-Exercise (More Than One Correct Option Type Questions)
  1. Three vectors veca,vecb,vecc are such that vecaxxvecb= 3(vecaxxvecc)Al...

    Text Solution

    |

  2. Let a, b and c be non-zero vectors and |a|=1 and r is a non-zero vecto...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  6. If vec a=x hat i+y hat j+z hat k , vec b=y hat i+z hat j+x hat k. The ...

    Text Solution

    |

  7. Which of the following statement(s) is/are true?

    Text Solution

    |

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

    Text Solution

    |

  9. If a,b and c are three non-zero vectors, then which of the following s...

    Text Solution

    |

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

    Text Solution

    |

  11. If a and b are any two unit vectors, then the possible integers in the...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  15. Find the nth term of AP whose first term is 12 and common difference i...

    Text Solution

    |

  16. Given three vectors a,b and c are non-zero and non-coplanar vectors. T...

    Text Solution

    |

  17. Find the nth term of GP if the first term is 7 and common ratio is 3.

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |