Home
Class 12
MATHS
Two adjacent sides of a parallelogram ...

Two adjacent sides of a parallelogram `A B C D` are given by ` vec A B=2 hat i+10 hat j+11 hat ka n d vec A D=- hat i+2 hat j+2 hat kdot` The side `A D` is rotated by an acute angle `alpha` in the plane of the parallelogram so that `A D` becomes `A D^(prime)dot` If `A D '` makes a right angle with the side `A B ,` then the cosine of the angel `alpha` is given by a. `8/9` b. `(sqrt(17))/9` c. `1/9` d. `(4sqrt(5))/9`

A

`(8)/(9)`

B

`(sqrt(17))/(9)`

C

`(1)/(9)`

D

`(4sqrt(5))/(9)`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • PRODUCT OF VECTORS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Subjective Type Questions)|17 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

Two adjacent sides of a parallelogram A B C D are given by vec A B=2 hat i+10 hat j+11 hat ka n d vec A D=- hat i+2 hat j+2 hat kdot The side A D is rotated by an acute angle alpha in the plane of the parallelogram so that A D becomes A D^(prime)dot If A D ' makes a right angle with the side A B , then the cosine of the angel alpha is given by 8/9 b. (sqrt(17))/9 c. 1/9 d. (4sqrt(5))/9

Find vec axx vec b ,\ if\ vec a=2 hat i+ hat k\ a n d\ vec b= hat i+ hat j+ hat kdot

Find vec adot vec b when: vec a= hat i-2 hat j+ hat k\ a n d\ vec b=4 hat i-4 hat j+7 hat k

Find the area of a parallelogram whose adjacent sides are given by the vectors vec a=3 hat i+ hat j+4 hat k and vec b= hat i- hat j+ hat k .

Find vec adot vec b when: vec a= hat j- hat k\ a n d\ vec b=2 hat i+3 hat j-2 hat k

The adjacent sides of a parallelogram are represented by the vectors vec a= hat i+ hat j- hat k\ a n d\ vec b=-2 hat i+ hat j+2 hat kdot Find unit vectors parallel to the diagonals of the parallelogram.

Find the angle between the vectors vec a= hat i- hat j+ hat k\ a n d\ vec b= hat i+ hat j- hat kdot

Find the area of the parallelogram whose adjacent sides are determined by the vectors vec a= hat i- hat j+3 hat ka n d vec b=2 hat i-7 hat j+ hat kdot

Find the unit vector in the direction of vec a+ vec b ,\ if\ vec a=2 hat i- hat j+2 hat k\ a n d\ vec b=- hat i+ hat j- hat kdot

Find the area of the parallelogram determined by the vectors hat i+2 hat j+3 hat ka n d3 hat i-2 hat j+ hat kdot

ARIHANT MATHS ENGLISH-PRODUCT OF VECTORS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. The vector(s) which is/are coplanar with vectors hat i+ hat j+2 hat...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  15. The value of a so that the volume of parallelepiped formed by hat i...

    Text Solution

    |

  16. If vec a=( hat i+ hat j+ hat k), vec a. vec b=1a n d vec axx vec b= h...

    Text Solution

    |

  17. Let vec V=2 hat i+ hat j- hat ka n d vec W= hat i+3 hat kdot If vec ...

    Text Solution

    |

  18. If veca and vecb are two unit vectors such that veca + 2vecb and 5 vec...

    Text Solution

    |

  19. Let a= 2hat(i) -2hat(k) , b=hat(i) +hat(j) and c be a vectors suc...

    Text Solution

    |

  20. If [axxb bxxc c xxa]=lambda[abc]^(2), then lambda is equal to

    Text Solution

    |