Home
Class 12
MATHS
If the position vectors off A,B,C and D ...

If the position vectors off A,B,C and D are `2hati+hatj,hati-3hatj,3hati+2hatj and hati+lamdahatj`, respectively and `AB||CD`, then `lamda` will be

A

`-8`

B

`-6`

C

8

D

6

Text Solution

Verified by Experts

The correct Answer is:
B
`AB=-hati-4hatj,CD=-2hati+(lamda-2)hatj`
`because AB||CD`
So, `(-1)/(-2)=(-4)/(lamda-2)implies lamda-2=-8`
`implies lamda=-6`
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 the position vectors of A,B,C and D are 2hati+hatj,hati-3hatj,3hati+2hatj and hati+lamda hatj respectively and |AB||CD. Then lamda will be

The position vectors of A,B,C are 2hati+hatj-hatk,3hati-2hatj+hatk and hati+4hatj-3hatk respectively. Show that A, B and C are collinear.

The position vectors of A and B are 2hati-9hatj-4hatk and 6hati-3hatj+8hatk respectively, then the magnitude of AB is

If the position vectors of A and B respectively hati+3hatj-7hatk and 5 hati-2hatj+4hatk , then find AB

If the position vectors of P and Q are (hati+3hatj-7hatk) and (5hati-2hatj+4hatk) , then |PQ| is

The position vectors of the points A,B and C are hati+2hatj-hatk,hati+hatj+hatk and 2hati+3hatj+2hatk , respectively. If A is chosen as the origin, then the position vectors of B and C are

The position vectors of the points A, B, C are 2 hati + hatj - hatk , 3 hati - 2 hatj + hatk and hati + 4hatj - 3 hatk respectively . These points

If the position vectors of the point A and B are : 7hati+3hatj-hatk and 2hati-5hatj+4hatk respectively, find the magnitude and direction-cosines of the vector vec(AB) .

The position vectors of the vertices of /_\ABC are : 3hati-4hatj-4hatk,2hati-hatj+hatk and hati-3hatj-5hatk respectively. Find vec(AB),vec(BC) and vec(CA) .

If the position vectors of A and B are hati+3hatj-7hatk and 5hati-2hatj+4hatk , then the direction cosine of AB along Y-axis is

ARIHANT MATHS-VECTOR ALGEBRA-Exercise (Single Option Correct Type Questions)
  1. The vectors hati+2hatj+3hatk,lamdahati+4hatj+7hatk,-3hati-2hatj-5hatk ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  6. Four non-zero vectors will always be

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  20. If P and Q are the middle points of the sides BC and CD of the paralle...

    Text Solution

    |