Home
Class 12
MATHS
The edges of a parallelopiped are of uni...

The edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vectors `hat(a), hat(b), hat(c)` such that `hat(a)*hat(b)=hat(b)*hat(c)=hat(c)*hat(a)=(1)/(2).` Then, the volume of the parallelopiped is

A

`(1)/(sqrt(2))` cu units

B

`(1)/(2sqrt(2))` cu units

C

`(sqrt(3))/(2)` cu units

D

`(1)/(sqrt(3))` cu units

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • PRODUCT OF VECTORS

    ARIHANT MATHS|Exercise Exercise (Subjective Type Questions)|18 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

The deges of a parallelopied are of unit length and are parallel to non- coplanar unit vector hat(a), hat(b) , hat(c ) such that hat(a) , hat(b) = hat(b), hat( c)=hat(c ), hat(a) = .(1)/(2). Then the volume of the parallelopiped is

The edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vectors vec a, vec b, vec c such that hat a.hatb=hatb .hatc=hatc.hata=1/2. Then, the volume of parallelopiped is

The edges of a parallelopiped of unit length are parallal to non-coplanar unit vectors widehat a,hat b,hat c such that widehat a.hat b=hat b*hat c=hat c.widehat a=1/2, then the volume of parallelopiped whose edges are widehat a xxhat b,hat b xxhat chat c xx widehat a is

If theta is the angle between two unit vectors hat(a) and hat(b) then (1)/(2)|hat(a)-hat(b)|=?

Find the altitude of a parallelopiped whose three conterminous edges are verctors A=hat(i)+hat(j)+hat(k), B=2hat(i)+4hat(j)-hat(k) and C=hat(i)+hat(j)+3hat(k) with A and B as the sides of the base of the parallelopiped.

If the vectors ahat(i)+hat(j)+hat(k), hat(i)+bhat(j)+hat(k), hat(i)+hat(j)+chat(k) , where a, b, c are coplanar, then a+b+c-abc=

The unit vector parallel to the resultant of the vectors vec(A) = hat(i) + 2 hat(j) - hat(k) and vec(B) = 2 hat(i) + 4 hat(j) - hat(k) is

Find a unit vector perpendicular to A=2hat(i)+3hat(j)+hat(k) and B=hat(i)-hat(j)+hat(k) both.

If the vectors (ahat(i)+a hat(j)+chat(k)), (hat(i)+hat(k)) and (c hat(i)+c hat(j)+b hat(k)) be coplanar, show that c^(2)=ab .

If vectors ahat(i)+hat(j)+hat(k),hat(i)+bhat(j)+hat(k),hat(i)+hat(j)+chat(k) are coplanar, then a+b+c-abc= . . . . . . . .

ARIHANT MATHS-PRODUCT OF VECTORS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If a and b are vectors in space given by a=(hat(i)-2hat(j))/(sqrt(5)) ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  4. Lelt two non collinear unit vectors hata and hatb form and acute angle...

    Text Solution

    |

  5. Let the vectors PQ, QR, RS, ST, TU and UP represent the sides of a reg...

    Text Solution

    |

  6. The number of distinct real values of lambda, for which the vectors -l...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  9. Let a=hat(i)+2hat(j)+hat(k), b=hat(i)-hat(j)+hat(k), c=hat(i)+hat(j)-h...

    Text Solution

    |

  10. If vec a , vec b and vec c are three non-zero, non coplanar vecto...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  15. If veca and vecb are two unit vectors such that veca+2vecb and 5veca-4...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  18. Let hata and hatb be two unit vectors. If the vectors vecc=hata+2hatb ...

    Text Solution

    |

  19. Let ABCD be a parallelogram such that vec AB = vec q,vec AD = vec p a...

    Text Solution

    |

  20. 1/sqrt(10)(3hatj + hatk) and vecb =(2hati +3hatj-6hatk), then the valu...

    Text Solution

    |