Home
Class 12
MATHS
A non-zero vecto veca is such tha its pr...

A non-zero vecto `veca` is such tha its projections along vectors `(hati + hatj)/sqrt2, (-hati + hatj)/sqrt2 and hatk` are equal , then unit vector along `veca` us

A

`(sqrt2hatj-hatk)/sqrt3`

B

`(hatj-sqrt2hatk)/sqrt3`

C

`sqrt2/sqrt3hatj+hatk/sqrt3`

D

`(hatj - hatk)/(sqrt2)`

Text Solution

Verified by Experts

The correct Answer is:
a
Let the projection be x then ,
`veca= (x(hati +hatj))/sqrt2+(x(-hati+hatj))/sqrt2+xhatk`
`veca= (2xhatj)/sqrt2+ xhatk or hata= sqrt2/sqrt3hatj + hatk/sqrt3`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Reasoning type|8 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Comprehension type|27 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Exercises|15 Videos

  • DETERMINANTS

    CENGAGE ENGLISH|Exercise All Questions|264 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE ENGLISH|Exercise Matrix Match Type|5 Videos
CENGAGE ENGLISH-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercises MCQ
  1. If a is real constant A ,Ba n dC are variable angles and sqrt(a^2-4)ta...

    Text Solution

    |

  2. The vertex A triangle A B C is on the line vec r= hat i+ hat j+lambda...

    Text Solution

    |

  3. A non-zero vecto veca is such tha its projections along vectors (hati ...

    Text Solution

    |

  4. Position vector hatk is rotated about the origin by angle 135^(@) in ...

    Text Solution

    |

  5. In a quadrilateral A B C D , vec A C is the bisector of vec A Ba n d ...

    Text Solution

    |

  6. In AB, DE and GF are parallel to each other and AD, BG and EF ar para...

    Text Solution

    |

  7. Vectors hata in the plane of vecb = 2 hati +hatj and vecc = hati-hatj ...

    Text Solution

    |

  8. Let A B C D be a tetrahedron such that the edges A B ,A Ca n dA D ar...

    Text Solution

    |

  9. Let vecf(t)=[t] hat i+(t-[t]) hat j+[t+1] hat k , w h e r e[dot] deno...

    Text Solution

    |

  10. If veca is parallel to vecb xx vecc, then (veca xx vecb) .(veca xx vec...

    Text Solution

    |

  11. The three vectors hat i+hat j,hat j+hat k, hat k+hat i taken two at a ...

    Text Solution

    |

  12. If vecd=vecaxxvecb+vecbxxvecc+vecc+veccxxveca is a non- zero vector an...

    Text Solution

    |

  13. If |veca|=2 and |vecb|=3 and veca.vecb=0, " then " (vecaxx(vecaxx(veca...

    Text Solution

    |

  14. If two diagonals of one of its faces are 6hati + 6 hatk and 4 hatj + ...

    Text Solution

    |

  15. The volume of a tetrahedron fomed by the coterminus edges veca , vecb ...

    Text Solution

    |

  16. If veca ,vecb and vecc are three mutually orthogonal unit vectors , th...

    Text Solution

    |

  17. vector vecc are perpendicular to vectors veca= (2,-3,1) and vecb= (1,...

    Text Solution

    |

  18. Given veca=xhati+yhatj+2hatk,vecb=hati-hatj+hatk , vecc=hati+2hatj, ve...

    Text Solution

    |

  19. Let veca=a(1)hati+a(2)hatj+a(3)hatk,vecb=b(1)hati+b(2)hatj+b(3)hatk an...

    Text Solution

    |

  20. Let vecr, veca, vecb and vecc be four non-zero vectors such that vecr....

    Text Solution

    |