Home
Class 12
MATHS
Let alpha, beta and gamma be distinct r...

Let `alpha, beta and gamma` be distinct real numbers. The points whose position vector's are `alpha hat i + beta hat j+gamma hat k; beta hat i+gamma hat j+alpha hat k and gamma hat i+alpha hat j+beta hat k` a. are collinear. b. forms an equilateral triangle. c. forms a scalene triangle. d. forms a right angled triangle.

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

If points hat i+ hat j , hat i- hat j and p hat i+q hat j+r hat k are collinear, then

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.

Show that the point A , B and C with position vectors vec a =3 hat i - 4 hat j -4 hat k vec b = 2 hat i - hat j + hat k and vec c = hat i - 3 hat j - 5 hat k , respectively form the vertices of a right angled triangle.

Show that the vectors are mutually perpendicular hat (i) + 2 hat (j) + hat (k) ,hat (i) + hat (j) - 3 hat (k) and 7 hat (i) - 4 hat (j) + hat (k)

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)

If the vectors vecalpha=a hat i+a hat j+c hat k , vecbeta= hat i+ hat k and vec gamma=c hat i+c hat j+b hat k are coplanar, then prove that c is the geometric mean of a and b.

Find the value of lambda for which the three points with position vector 3 hat i-2 hat j- hat k ,2 hat i+3 hat j-4 hat k , and4 hat i+5 hat j+lambda hat k are coplanar.

If vectors vec a= hat i+2 hat j- hat k , vec b=2 hat i- hat j+ hat k and vec c=lambda hat i+ hat j+2 hat k are coplanar, then find the value of (lambda-4) .

In each of the following show that the given vectors are coplanar: 4 hat (i) + 2 hat (j) + hat (k) , 2 hat (i) - hat (j) + 3 hat (k) , 8 hat (i) + 7 hat (k)

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

CENGAGE PUBLICATION-VECTOR ALGEBRA-All Questions
  1. If the vectors vecalpha=a hat i+a hat j+c hat k , vecbeta= hat i+ hat...

    Text Solution

    |

  2. The points with position vectors 60 i+3j ,40 i-8j ,a i-52 j are col...

    Text Solution

    |

  3. Let alpha, beta and gamma be distinct real numbers. The points whose ...

    Text Solution

    |

  4. Let vec a= vec i- vec k , vec b=x vec i+ vec j+(1-x) vec k and vec c...

    Text Solution

    |

  5. In the DeltaOAB,M is the mid-point of AB,C is a point on OM, such that...

    Text Solution

    |

  6. If vec a , vec b are two non-collinear vectors, prove that the poi...

    Text Solution

    |

  7. If vec a= hat i+ hat j+ hat k , vec b=4 hat i+3 hat j+4 hat k and ve...

    Text Solution

    |

  8. The number of distinct real values of lambda , for which the vectors...

    Text Solution

    |

  9. If vec A O+ vec O B= vec B O+ vec O C , then A ,B and C are (where O...

    Text Solution

    |

  10. Find a vector magnitude 5 units, and parallel to the resultant of t...

    Text Solution

    |

  11. Show that the points A(1,-2,-8),B(5,0,-2)a n dC(11,3,7) are collinear,...

    Text Solution

    |

  12. The position vectors of Pa n dQ are 5 hat i+4 hat j+a hat k and - hat ...

    Text Solution

    |

  13. Given three points are A(-3,-2,0),B(3,-3,1)a n dC(5,0,2)dot Then find ...

    Text Solution

    |

  14. Let A B C D be a p[arallelogram whose diagonals intersect at P and ...

    Text Solution

    |

  15. If A B C D is quadrilateral and Ea n dF are the mid-points of A Ca n d...

    Text Solution

    |

  16. If A B C D is a rhombus whose diagonals cut at the origin O , then p...

    Text Solution

    |

  17. Let D ,Ea n dF be the middle points of the sides B C ,C Aa n dA B , re...

    Text Solution

    |

  18. Consider the set of eight vectors V[ahati+bhatj+chatk:a,b,c in {1-1}]....

    Text Solution

    |

  19. Find the direction cosines of the vector joining the points A(1,2,-...

    Text Solution

    |

  20. Find the direction cosines of the vector hat i+2 hat j+3 hat kdot

    Text Solution

    |