Home
Class 12
MATHS
If the points a+b,a-b and a+kb be collin...

If the points `a+b,a-b and a+kb` be collinear, then k is equal to

A

A. 0

B

B. 2

C

C. `-2`

D

D. any real number

Text Solution

Verified by Experts

The correct Answer is:
D
`(a-b)-(a+b)=[(a+kb)-(a-b)]`
`implies -2b=(k+1)b`
Hence, `k in R`
Promotional Banner

Topper's Solved these Questions

  • VECTOR ALGEBRA

    ARIHANT MATHS|Exercise VECTOR ALGEBRA EXERCISES 1: Single Option Correct Type Questions|1 Videos

  • VECTOR ALGEBRA

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|7 Videos

  • VECTOR ALGEBRA

    ARIHANT MATHS|Exercise Exercise For Session 3|11 Videos

  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

Similar Questions

Explore conceptually related problems

If points (a, 0), (0, b) and (x, y) are collinear, then write correct answer from the following :

Prove that the points (a, b), (c, d) and (a-c, b-d) are collinear, if ad = bc.

If the points (x,y),(a,0) and (0,b) are collinear, prove that x/a + y/b = 1, ab ne 0

Statement 1: if three points P ,Qa n dR have position vectors vec a , vec b ,a n d vec c , respectively, and 2 vec a+3 vec b-5 vec c=0, then the points P ,Q ,a n dR must be collinear. Statement 2: If for three points A ,B ,a n dC , vec A B=lambda vec A C , then points A ,B ,a n dC must be collinear.

If the position vectors of the points A,B and C be a,b and 3a-2b respectively, then prove that the points A,B and C are collinear.

Prove that the points (a,b), (a'b'), (a-a',b-b') are collinear iff ab' = a'b.

Prove that the points (a ,b+c),(b ,c+a)a n d(c ,a+b) are collinear.

Let a,b,c are three vectors of which every pair is non-collinear, if the vectors a+b and b+c are collinear with c annd a respectively, then find a+b+c.

If three points (h, 0), (a, b) and (0, k) lies on a line, show that a/h+b/k=1

If a,b and c are three non-zero vectors such that no two of these are collinear. If the vector a+2b is collinear with c and b+3c is collinear with a( lamda being some non-zero scalar), then a+2b+6c is equal to

ARIHANT MATHS-VECTOR ALGEBRA-Exercise (Single Option Correct Type Questions)
  1. The points with position vectors 10hati+3hatj,12hati-5hatj and ahati+1...

    Text Solution

    |

  2. The vectors hati+2hatj+3hatk,lamdahati+4hatj+7hatk,-3hati-2hatj-5hatk ...

    Text Solution

    |

  3. If the points a+b,a-b and a+kb be collinear, then k is equal to

    Text Solution

    |

  4. If the position vectors off A,B,C and D are 2hati+hatj,hati-3hatj,3hat...

    Text Solution

    |

  5. If the vectors 3hati+2hatj-hatk and 6hati-4xhatj+yhatk are parallel, t...

    Text Solution

    |

  6. If a and b are two non collinear vectors; then every vector r coplanar...

    Text Solution

    |

  7. Four non-zero vectors will always be

    Text Solution

    |

  8. The vectors a,b and a+b are

    Text Solution

    |

  9. Find the all the values of lamda such that (x,y,z)!=(0,0,0)and x(hati+...

    Text Solution

    |

  10. The number of integral values of p for which (p+1) hati-3hatj+phatk, p...

    Text Solution

    |

  11. If the vectors AB=3hati+4hatk and AC=5hati-2hatj+4hatk are the sides o...

    Text Solution

    |

  12. In the figure, a vectors x satisfies the equation x-w=v. then, x is eq...

    Text Solution

    |

  13. Vectors veca = hati+2hatj+3hatk, vec b = 2hati-hatj+hatk and vecc= 3ha...

    Text Solution

    |

  14. If OP=8 and OP makes angles 45^(@) and 60^(@) with OX-axis and OY-axis...

    Text Solution

    |

  15. Let a,b and c be three unit vectors such that 3a+4b+5c=0. Then which o...

    Text Solution

    |

  16. if A,B,C,D and E are five coplanar points, then vec(DA) + vec( DB) + v...

    Text Solution

    |

  17. If the vectors veca and vecb are linearly independent satisfying (sqrt...

    Text Solution

    |

  18. Find the slope of the normal having point (3,2) and (4,1)

    Text Solution

    |

  19. A line passes through the points whose position vectors are hati+hatj-...

    Text Solution

    |

  20. Find the slop of line . The Equation of line is 2x-3y=2

    Text Solution

    |