Home
Class 12
MATHS
If A(-4,0,3) and B(14 ,2,-5), then which...

If `A(-4,0,3) and B(14 ,2,-5),` then which one of the following points lie on the bisector of the angle between ` vec OA and vec OB (O` is the origin of reference )?
a. `(2,2,4)` b. `(2, 11 ,5)` c. `(-3,-3,-6)` d. `(1,1,2)`

A

(2,2,4)

B

(2,11,5)

C

(-3,-3,-6)

D

(1,1,2)

Text Solution

Verified by Experts

`OA=-4hati+3hatk,OB=14hati+2hatj-5hatk`
`a=(-4hati+3hatk)/(5),b=(14hati+2hatj-5hatk)/(15)`
`r=(lamda)/(15)[12hati+9hatj+14 hati+2hatj-5hatk]`
`=(lamda)/(15)[2hati+2hatj+4hatk]=(2lamda)/(15)[hati+hatj+2hatk]`.
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

A(3,-1,2),B(2,-3,3) and C(1,-2,1) are three given points . Find the angle between the vectors vec(BA)and vec(BC) .

If | vec a+ vec b|<| vec a- vec b|, then the angle between vec aa n d vec b can lie in the interval a. (pi//2,pi//2) b. (0,pi) c. (pi//2,3pi//2) d. (0,2pi)

A(1,3,0),B(2,2,1) and C(5,-1,4) are the vertices of the triangle ABC, if the bisector of /_BAC meets its side bar(BC) at D, then find the coordinates of D.

Let vec a= hat i+ hat j and vec b=2 hat i- hat k , then the point of intersection of the lines vec rxx vec a= vec bxx vec a and vec rxx vec b= vec axx vec b is a. (3,-1,1) b. (3,1,-1) c. (-3,1,1) d. (-3,-1,-1)

If 2vec(AC)=3vec(CB) , then prove that 2vec(OA)+3vec(OB)=5vec(OC) where O is the origin.

If |vec(a)|= 3 , |vec(b)| = 4 and | vec (a) xx vec(b)|= 6 , then find the angle between the vectors vec(a) and vec(b)

If vec a and vec b are unit vectors such that ( vec a+ vec b).[(2 vec a+3 vec b)xx(3 vec a-2 vec b)]=0 , then angle between veca and vec b is

If | vec(a)|= 4 , |vec(b)| = 2 sqrt(3) and |vec(a) xx vec(b)| = 12, then the angle between the vectors vec (a) and vec (b) is -

The centre of the circle given by vec r.( hat i+2 hat j+2 hat k)=15a n d| vec r.( hat j+2 hat k)|=4 is a. (0,1,2) b. (1,3,4) c. (-1,3,4) d. none of these

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)

CENGAGE PUBLICATION-VECTOR ALGEBRA-All Questions
  1. Let A B C be a triangle, the position vectors of whose vertices are -1...

    Text Solution

    |

  2. If non-zero vectors vec a and vec b are equally inclined to coplanar ...

    Text Solution

    |

  3. If A(-4,0,3) and B(14 ,2,-5), then which one of the following points l...

    Text Solution

    |

  4. Prove that the sum of three vectors determined by the medians of a ...

    Text Solution

    |

  5. Prove that the resultant of two forces acting at point O and repres...

    Text Solution

    |

  6. Two forces vec A B and vec A D are acting at vertex A of a quadrilat...

    Text Solution

    |

  7. ABC is a triangle and P any point on BC. If vec(PQ) is the sum of vec(...

    Text Solution

    |

  8. If vector vec a+ vec b bisects the angle between vec a and vec b , ...

    Text Solution

    |

  9. ABCDE is a pentagon. Prove that the resultant of force vec A B , vec...

    Text Solution

    |

  10. if vec (AO) + vec (O B) = vec (B O) + vec (O C) ,than prove that B...

    Text Solution

    |

  11. A unit vector of modulus 2 is equally inclined to x- and y-axes at an ...

    Text Solution

    |

  12. Find the equations of the normal to the curve y=x^3+2x+6 which are par...

    Text Solution

    |

  13. Let vec a , vec b and vec c be unit vectors such that vec a+ vec b- ...

    Text Solution

    |

  14. If the resultant of three forces vec F1=p hat i+3 hat j- hat k , ve...

    Text Solution

    |

  15. Let vec a , vec b , vec c , vec d be the position vectors of the four...

    Text Solution

    |

  16. Statement 1:Let A( vec a),B( vec b)a n dC( vec c) be three points such...

    Text Solution

    |

  17. Statement 1: If | vec a+ vec b|=| vec a- vec b|, then vec a and vec b ...

    Text Solution

    |

  18. Statement 1: vec a=3 vec i+p vec j+3 vec k and vec b=2 vec i+3 vec j...

    Text Solution

    |

  19. The position vectors of the vertices A ,Ba n dC of a triangle are th...

    Text Solution

    |

  20. If | vec a|=| vec b|=| vec a+ vec b|=1, then find the value of | vec a...

    Text Solution

    |