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 `8/9` b. `(sqrt(17))/9` c. `1/9` d. `(4sqrt(5))/9`

A

`8/9`

B

`sqrt 17/9`

C

`1/9`

D

`4 sqrt 5/9`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • Miscellaneous Exercises

    A DAS GUPTA|Exercise Exercise|77 Videos

  • Pair of Straight Lines and Transformation of Axes

    A DAS GUPTA|Exercise EXERCISE|22 Videos

Similar Questions

Explore conceptually related problems

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

Angle between diagonals of a parallelogram whose side are represented by vec a=2hat i+hat j+hat k and vec b=hat i-hat j-hat k

If vec a=3 hat i- hat j+2 hat k\ a n d\ vec b=2 hat i+ hat j- hat k\ t h e n find ( vec axx vec b) vec adot

Determine the area of the parallelogram whose adjacent sides are formed by the vectors vec A = hat i -3 hat j + hat k and vec B = hat i + hat j + hat k .

If in parallelogram ABCD, diagonal vectors are vec A C=2 hat i+3 hat j+4 hat k and vec B D=-6 hat i+7 hat j-2 hat k , then find the adjacent side vectors vec A B and vec A D

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

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

The diagonals if a parallele-gram are representde by vec d_(1) =2 hat I + 3 hat j -5 hat k and vec d_(2) =6 hat I + 5 hat j -3 hat k . Find the area of the parallelogram.

The adjacent sides of a parallelogram is represented by vectors 2hat(i)+3 hat(j) and hat(i) +4 hat(j) . The area of the parallelogram is :

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

A DAS GUPTA-Objective Tests-Exercise
  1. An ellipse intersects the hyperbola 2x^(2)-2y^(2)=1 orthogonally. The ...

    Text Solution

    |

  2. Let L = lim(x rarr 0) ( a - sqrt( a^2 - x^2) - x^2/4)/x^4, a>0.If L is...

    Text Solution

    |

  3. For the function f(x)=x "cos" 1/x, x ge1

    Text Solution

    |

  4. If In=int(-pi)^(pi) \ (sinnx)/((1+pi^x) \ sinx) \ dx, n=0,1,2,...... t...

    Text Solution

    |

  5. The area of the region bounded by the curve y=e^(x) and lines x=0 and ...

    Text Solution

    |

  6. Q. Let p and q real number such that p!= 0,p^2!=q and p^2!=-q. if alph...

    Text Solution

    |

  7. Let S={1,,2,34} . The total number of unordered pairs of disjoint s...

    Text Solution

    |

  8. For r= 0, 1,.....,10, let Ar,Br, and Crdenote, respectively, the coe...

    Text Solution

    |

  9. The number of 3xx3 matrices A whose entries are either 0or1 and for wh...

    Text Solution

    |

  10. If the angle A , B and C of a triangle are in arithmetic progession an...

    Text Solution

    |

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

    Text Solution

    |

  12. The equation of the plane containing the straight line x/2=y/3=z/4 and...

    Text Solution

    |

  13. If the distance of the point P(1,-2,1) from the plane x+2y-2z=alpha...

    Text Solution

    |

  14. Let f,g and h be real-valued functions defined on the interval [0,1] b...

    Text Solution

    |

  15. Let f be a real-valued function defined on the inverval (-1,1) such th...

    Text Solution

    |

  16. Let omega be a complex cube root unity with omega!=1. A fair die is th...

    Text Solution

    |

  17. A signal which can be green or red with probability 4/5 and 1/5 respec...

    Text Solution

    |

  18. Let z(1) and z(2) be two distinct complex numbers and z=(1-t)z(1)+iz(2...

    Text Solution

    |

  19. Let ABC be a triangle such that angleACB=pi/6 and let a , b and c deno...

    Text Solution

    |

  20. Let A and B be two distinct points on the parabola y^2 = 4x. If the ax...

    Text Solution

    |