Home
Class 12
MATHS
If a, b, c and d are the unit vectors su...

If a, b, c and d are the unit vectors such that `(atimesb)*(ctimesd)=1 and a*c=(1)/(2)`, then

A

`veca,vecb,vecc` are non-coplanar

B

`vecb,vecc,vecd` are non-coplanar

C

`vecb,vecd` are non-parallel

D

`veca,vecd` and parallel and `vecb,vecc` are parallel.

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • VECTORS

    MODERN PUBLICATION|Exercise Exercise|500 Videos

  • UNIT TEST-4

    MODERN PUBLICATION|Exercise EXERCISE|13 Videos

Similar Questions

Explore conceptually related problems

Let a, b and c be three unit vectors such that atimes(btimesc)=(sqrt(3))/(2)(b+c) . If b is not parallel to c , then the angle between a and b is

Q8) Ifa, b, c (b, care non-parallel) are unit vectors such that a x ( b × c ) = (1/2) then the angle which a makes with b and are en the angle which a makes with b and c are A. 30, 60 B. 600, 90° C. 90, 60 D. 60°, 30°

Three vectors a(|a|ne0), b and c are such that atimesb=3atimesc , also |a|=|b|=1 and |c|=(1)/(3) . If the angle between b and c is 60^(@) and |b-3c|=lambda|a| , then the value of lambda is

If vec a , vec b , vec c are unit vectors such that vec adot vec b=0= vec adot vec c and the angle between vec ba n d vec c is pi//3 , then the value of | vec axx vec b- vec axx vec c| is 1//2 b. 1 c. 2 d. none of these

Let a,b and c be three unit vectors such that 3a+4b+5c=0 . Then which of the following statements is true?

If a, b and c are three vectors such that [a b c]=1, then find the value of [a+b b+c c+a]+[ atimesb btimesc ctimesa ]

If a, b, c and a', b', c' are recoprocal system of vectors, then prove that a'timesb'+b'timesc'+c'timesa'=(a+b+c)/([a b c]) .

If a, b and c be the three non-zero vectors satisfying the condition atimesb=c and btimesc=a , then which of the following always hold(s) good?

Let a, b and c be non-zero vectors and |a|=1 and r is a non-zero vector such that r times a=b and r*a=1 , then a. abotb b. rbotb c. r*a=(1-[a b c])/(a*b) d. [r a b]=0

If a,b,c and d are four positive real numbers such that abcd=1 , what is the minimum value of (1+a)(1+b)(1+c)(1+d) .

MODERN PUBLICATION-VECTORS-Exercise
  1. The non-zero vectors veca,vecb and vecc are related by veca=8vecb and ...

    Text Solution

    |

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

    Text Solution

    |

  3. If a, b, c and d are the unit vectors such that (atimesb)*(ctimesd)=1 ...

    Text Solution

    |

  4. If vecu, vecv, vecw are non -coplanar vectors and p,q, are real numbe...

    Text Solution

    |

  5. Let veca =hatj-hatk and vecc =hati-hatj-hatk. Then the vector b satisf...

    Text Solution

    |

  6. If the vectors veca=hati-hatj+2hatk.vecb=2hati+4hatj+hatk and vec c=la...

    Text Solution

    |

  7. The vectors veca and vecb are not perpendicular and vecc and vecd are ...

    Text Solution

    |

  8. Let veca=hati+hatj+hatk, vecb=hati-hatj+hatk and vecc=hati-hatj-hatk b...

    Text Solution

    |

  9. If the vectors phati+hatj+hatk,hati+qhatj+hatk and hati+hatj+rhatk(p n...

    Text Solution

    |

  10. Let a,b and c be three non-zero vectors which are pairwise non-colline...

    Text Solution

    |

  11. Let veca and vecb be two unit vectors. If the vectors : vecc=veca+2vec...

    Text Solution

    |

  12. Let ABCD be a parallelogram such that AB=q, AD=p and angleBAD be an ac...

    Text Solution

    |

  13. If veca and vecb are vectors such that |veca+vecb|=sqrt(29) and vecaxx...

    Text Solution

    |

  14. If the vectors vec(AB)=3hati+4hatk and vec(AC)=5hati-2hatj-4hatk are t...

    Text Solution

    |

  15. Let vec(PR)=3hati+hatj-2hatk and vec(SQ)=hati-3hatj-4hatk determine di...

    Text Solution

    |

  16. If [vecaxxvecb vecbxxvecc veccxxveca]=lambda[veca vecb vecc]^2, ...

    Text Solution

    |

  17. Let veca,vecb and vecc be three non-zero vectors such that no two of t...

    Text Solution

    |

  18. Let veca,vecb and vecc be three unit vectors such that : vecaxx(vecbxx...

    Text Solution

    |

  19. Find the values of 'x' for which x(hati+hatj+hatk) is a unit vector.

    Text Solution

    |

  20. Find the angle between the vectors hati-hatj and hatj-hatk.

    Text Solution

    |