Home
Class 12
MATHS
Position vector hat k is rotated about ...

Position vector ` hat k` is rotated about the origin by angle `135^0` in such a way that the plane made by it bisects the angle between ` hat i` and `hatj`. Then its new position is

A

`+-hati/sqrt2+-hatj/sqrt2`

B

`+-hati/2+-hatj/2-hatk/sqrt2`

C

`hati/sqrt2-hatk/sqrt2`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
d
Let `vecr` be the new position . Then `vecr= lambdahatk + mu ( hati + hatj) `
` Also, vecr.hatk = - 1/sqrt2 Rightarrow lambda= - 1/sqrt2`
` Also lambda^(2)+ 2mu^(2) = 1 Rightarrow 2mu^92) = 1/2 or mu = +- 1/2`
` vecr = +- 1/2 (hati + hatj) =- hatk/sqrt2`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Reasoning type|8 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Comprehension type|27 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Exercises|15 Videos

  • DETERMINANTS

    CENGAGE PUBLICATION|Exercise All Questions|262 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|578 Videos

Similar Questions

Explore conceptually related problems

Find out the angle between two-vectors hat i + hat j and hat i- hat k .

Find the cosine of the angle made by the vector (2hat i-3hatj+6hatk) with the posititve z-axis.

Find the angle made by the vector sqrt(2) hat (i) + hat (j) + hat (k) with the y - axis

Find the scalar product of the following pair of vectors and the angle between them : hat (i) + hat(j) and hat (j) + hat (k)

Let A ,B ,C be points with position vectors 2 hat i- hat j+ hat k , hat i+2 hat j+3 hat ka n d3 hat i+ hat j+2 hat k respectively. Find the shortest distance between point B and plane O A Cdot

Find the angle of vector vec a = 6 hat i + 2 hat j - 3 hat k with x -axis.

The position vectors of the points Pa n dQ with respect to the origin O are vec a= hat i+3 hat j-2 hat k and vec b=3 hat i- hat j-2 hat k , respectively. If M is a point on P Q , such that O M is the bisector of angleP O Q , then vec O M is a. 2( hat i- hat j+ hat k) b. 2 hat i+ hat j-2 hat k c. 2(- hat i+ hat j- hat k) d. 2( hat i+ hat j+ hat k)

Find the angle between the vectors hat i-2 hat j+3 hat k and 3 hat i-2 hat j+ hat kdot

If vec a=7 hat i-4 hat j-4 hat k and vec b=-2 hat i- hat j+2 hat k , determine vector vec c along the internal bisector of the angle between of the angle between vectors vec a and vec b such that | vec c| =5sqrt(6)

Angle in (rad) made by the vector ( sqrt3 hat i +hat j ) with X-axis is:

CENGAGE PUBLICATION-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercises MCQ
  1. The vertex A triangle A B C is on the line vec r= hat i+ hat j+lambda...

    Text Solution

    |

  2. A non-zero vector vec a is such that its projections along vectors ...

    Text Solution

    |

  3. Position vector hat k is rotated about the origin by angle 135^0 in...

    Text Solution

    |

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

    Text Solution

    |

  5. In fig. A B ,D Ea n dG F are parallel to each other and A D ,B Ga n...

    Text Solution

    |

  6. Vector vec a in the plane of vec b=2 hat i+ hat ja n d vec c= hat i-...

    Text Solution

    |

  7. Let A B C D be a tetrahedron such that the edges A B ,A C and A D ar...

    Text Solution

    |

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

    Text Solution

    |

  9. If vec a is parallel to vec bxx vec c , then ( vec axx vec b).( vec ...

    Text Solution

    |

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

    Text Solution

    |

  11. If vec d= vec axx vec b+ vec bxx vec c+ vec cxx vec a is non-zero vec...

    Text Solution

    |

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

    Text Solution

    |

  13. If the two diagonals of one its faces are 6 hat i+6 hat ka n d4 hat ...

    Text Solution

    |

  14. The volume of a tetrahedron formed by the coterminous edges vec a ...

    Text Solution

    |

  15. If vec a , vec b , and vec c are three mutually orthogonal unit vector...

    Text Solution

    |

  16. Vector vec c is perpendicular to vectors vec a=(2,-3,1)a n d vec b...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  20. If veca, vecb and vecc are such that [veca \ vecb \ vecc] =1, vecc= la...

    Text Solution

    |