Home
Class 12
MATHS
If 4 hat i+7 hat j+8 hat k ,2 hat i+3 ha...

If `4 hat i+7 hat j+8 hat k ,2 hat i+3 hat j+4hat ja n d2 hat i+5 hat j+7 hat k` are the position vectors of the vertices `A ,Ba n dC ,` respectively, of triangle `A B C` , then the position vecrtor of the point where the bisector of angle `A` meets `B C` is a. `2/3(-6 hat i-8 hat j- hat k)` b. `2/3(6 hat i+8 hat j+6 hat k)` c. `1/3(6 hat i+13 hat j+18 hat k)` d. `1/3(5 hat j+12 hat k)`

Promotional Banner

Topper's Solved these Questions

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

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|6 Videos

  • VECTORS TRIPLE PRODUCTS, RECIPROCAL SYSTEM OF VECTORS

    CENGAGE PUBLICATION|Exercise DPP 2.4|20 Videos

Similar Questions

Explore conceptually related problems

find the projection of 3hat i - hat j + 4hat k on 2 hat i + 3 hat j -6 hat k

A uni-modular tangent vector on the curve x=t^2+2,y=4t-5,z=2t^2-6 at t=2 is a. 1/3(2 hat i+2 hat j+ hat k) b. 1/3( hat i- hat j- hat k) c. 1/6(2 hat i+ hat j+ hat k) d. 2/3( hat i+ hat j+ hat k)

If vec a= 2 hat i- hat j+ hat k and vec b = - hat i+3 hat j+4 hat k ,then veca.vecb =

If vec a=3 hat i- hat j-4 hat k , vec b=2 hat i+4 hat j-3 hat k and vec c= hat i+2 hat j- hat k , find |3 vec a-2 hat b+4 hat c|dot

The unit vector orthogonal to vector -hat i+ hat j+2 hat k and making equal angles with the x and y-axis a. +-1/3(2 hat i+2 hat j- hat k) b. +-1/3( hat i+ hat j- hat k) c. +-1/3(2 hat i-2 hat j- hat k) d. none of these

Find | -> axx -> b|, if -> a=2 hat i+ hat j+3 hat k and -> b=3 hat i+5 hat j-2 hat k .

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)

Prove that point hat i +2 hat j - 3 hat k ,2 hat i - hat j + hat k and 2 hat i + 5 hat j - hat k from a triangle in space.

Find the area of triangle whose vertices have position vectors hat (i) + hat (j) + 2 hat (k) , 2 hat (i) + 2 hat (j) + 3 hat (k) and 3 hat (i) - hat (j) - hat (k)

The sides of a parallelogram are 2 hat i+4 hat j-5 hat k and hat i+2 hat j+3 hat k . The unit vector parallel to one of the diagonals is a. 1/7(3 hat i+6 hat j-2 hat k) b. 1/7(3 hat i-6 hat j-2 hat k) c. 1/(sqrt(69))( hat i+6 hat j+8 hat k) d. 1/(sqrt(69))(- hat i-2 hat j+8 hat k)

CENGAGE PUBLICATION-VECTOR ALGEBRA-All Questions
  1. If vec xa n d vec y are two non-collinear vectors and A B C isa trian...

    Text Solution

    |

  2. If hat i-3 hat j+5 hat k bisects the angle between hat a and - hat ...

    Text Solution

    |

  3. If 4 hat i+7 hat j+8 hat k ,2 hat i+3 hat j+4hat ja n d2 hat i+5 hat j...

    Text Solution

    |

  4. If vec b is a vector whose initial point divides thejoin of 5 hat i...

    Text Solution

    |

  5. Find the value of lambda so that the points P ,Q ,R and S on the sides...

    Text Solution

    |

  6. A uni-modular tangent vector on the curve x=t^2+2,y=4t-5,z=2t^2-6 at...

    Text Solution

    |

  7. If vec xa n d vec y are two non-collinear vectors and a, b, and c r...

    Text Solution

    |

  8. The position vectors of points Aa n dB w.r.t. the origin are vec a=...

    Text Solution

    |

  9. What is the unit vector parallel to vec a=3 hat i+4 hat j-2 hat k ...

    Text Solution

    |

  10. ABCD  is a quadrilateral and  E  is the point of intersection of ...

    Text Solution

    |

  11. A straight line L cuts the lines A B ,A Ca n dA D of a parallelogram A...

    Text Solution

    |

  12. Find the vector of magnitude 3, bisecting the angle between the vec...

    Text Solution

    |

  13. If vec aa n d vec b are two vectors of magnitude 1 inclined at 120^0 ...

    Text Solution

    |

  14. If vec r1, vec r2, vec r3 are the position vectors of the collinear ...

    Text Solution

    |

  15. Examine the following vector for linear independence: (1) vec i+ve...

    Text Solution

    |

  16. Show that the vectors 2 vec a- vec b+3 vec c , vec a+ vec b-2 vec ca n...

    Text Solution

    |

  17. Let vec a , vec ba n d vec c be three units vectors such that 2 vec a...

    Text Solution

    |

  18. Four non –zero vectors will always be a.  linearly dependent       ...

    Text Solution

    |

  19. A boat moves in still water with a velocity which is k times less t...

    Text Solution

    |

  20. In a triangle P Q R ,Sa n dT are points on Q Ra n dP R , respectively,...

    Text Solution

    |