Home
Class 12
MATHS
The unit vector which is orthogonal to...

The unit vector which is orthogonal to the vector `3 hat j+2 hat j+6 hat k` and is coplanar with vectors `2 hat i+ hat j+ hat ka n d hat i- hat j+ hat k` is `(2 hat i-6 hat j+ hat k)/(sqrt(41))` b. `(2 hat i-3 hat j)/(sqrt(13))` c. `(3 hat j- hat k)/(sqrt(10))` d. `(4 hat i+3 hat j-3 hat k)/(sqrt(34))`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS

    CENGAGE ENGLISH|Exercise Multiple Correct Answers Type|6 Videos

  • VECTORS TRIPLE PRODUCTS, RECIPROCAL SYSTEM OF VECTORS

    CENGAGE ENGLISH|Exercise DPP 2.4|20 Videos

Similar Questions

Explore conceptually related problems

A unit vector parallel to the intersection of the planes vec r. \ ( hat i- hat j+ hat k)=5 \ a n d \ vec r. \ (2 hat i+ hat j-3 hat k)=4 a. (2 hat i+5 hat j-3 hat k)/(sqrt(38)) b. (-2 hat i+5 hat j-3 hat k)/(sqrt(38)) c. (2 hat i+5 hat j-3 hat k)/(sqrt(38)) d. (-2 hat i-5 hat j-3 hat k)/(sqrt(38))

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

Show that the vectors 2 hat i-3 hat j+4 hat k\ a n d-4 hat i+6 hat j-8 hat k are collinear.

Find the projection of the vector hat i+3 hat j+7 hat k on the vector 7 hat i- hat j+8 hat k

A unit vector perpendicular to both hat i+ hat j\ a n d\ hat j+ hat k is hat i- hat j+ hat k b. hat i+ hat j+ hat k c. 1/(sqrt(3))( hat i+ hat j+ hat k) d. 1/(sqrt(3))( hat i- hat j+ hat k)

Show that the vectors veca= hat i-2 hat j+3 hat k , vecb=-2 hat i+3 hat j-4 hat ka n d vec c= hat i-3 hat j+5 hat k are coplanar.

Find a vector of magnitude 9, which is perpendicular to both vectors 4 hat i- hat j+3 hat ka n d-2 hat i+ hat j-2 hat k .

If the vectors hat i- hat j , hat j+ hat k and vec a form a triangle, then vec a may be a. - hat i- hat k b. hat i-2 hat j- hat k c. 2 hat i+ hat j+ hat k d. hat i+ hat k

Find the direction cosines of the following vectors: 2 hat i+2 hat j- hat k 6 hat i-2 hat j-3 hat k 3 hat i-4 hat k

Find the direction cosines of the following vectors: 2 hat i+2 hat j- hat k 6 hat i-2 hat j-3 hat k 3 hat i-4 hat k

CENGAGE ENGLISH-VECTOR ALGEBRA-All Questions
  1. Let vec a= hat i+2 hat j+ hat k , vec b= hat i- hat j+ hat ka n d vec...

    Text Solution

    |

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

    Text Solution

    |

  3. The unit vector which is orthogonal to the vector 3 hat j+2 hat j+6 ...

    Text Solution

    |

  4. If vec a and vec b are unequal unit vectors such that ( vec a- vec ...

    Text Solution

    |

  5. If veca,vecb,vecc are 3 unit vectors such that vecaxx(vecbxxvecc)=vec...

    Text Solution

    |

  6. If in triangle A B C , vec A B= vec u/(| vec u|)- vec v/(| vec v|)a n ...

    Text Solution

    |

  7. A vector vec d is equally inclined to three vectors vec a= hat i+ ...

    Text Solution

    |

  8. If axx(bxxc)=(axxb)xxc , then ( vec cxx vec a)xx vec b= vec0 b. vec cx...

    Text Solution

    |

  9. If hat a , hat b ,a n d hat c are three unit vectors inclined to ea...

    Text Solution

    |

  10. Let the pairs a , b,and c ,d each determine a plane. Then the planes a...

    Text Solution

    |

  11. P(vec p) and Q(vec q) are the position vectors of two fixed points and...

    Text Solution

    |

  12. Two adjacent sides of a parallelogram A B C D are 2 hat i+4 hat j-5 ...

    Text Solution

    |

  13. If vec a and vec b are two unit vectors and theta is the angle between...

    Text Solution

    |

  14. If vec a , vec b , vec c are unit vectors such that vec adot vec b=0...

    Text Solution

    |

  15. Let vec a= hat i+ hat j ; vec b=2 hat i- hat kdot Then vector vec r ...

    Text Solution

    |

  16. If vec a and vec b are two vectors, such that vec a.vec b<0 and | ve...

    Text Solution

    |

  17. vec a , vec b , and vec c are three vectors of equal magnitude. The an...

    Text Solution

    |

  18. If vec a , vec ba n d vec c are three mutually perpendicular vect...

    Text Solution

    |

  19. Let vec aa n d vec b be two non-collinear unit vector. If vec u= vec...

    Text Solution

    |

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

    Text Solution

    |