Home
Class 12
MATHS
Show that the vectors veca=overset^^i-2...

Show that the vectors
`veca=overset^^i-2overset^^j+3overset^^k,vecb=-2overset^^i+3overset^^j-4overset^^k`and `vecc=overset^i-3overset^j+5overset^^k` are coplanar.

Text Solution

Verified by Experts

`veca.(vecbxxvecc)=|(1,-2,3),(-2,3,-4),(1,-3,5)|=0`
Hence, in view of theorem `1,veca,vecb"and"vecc` are coplanar vectors.
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSTIONAL GEOMETRY

    A N EXCEL PUBLICATION|Exercise QUESTION BANK|97 Videos

Similar Questions

Explore conceptually related problems

Find the volume of a parallelepiped with coterminal edges represented by vectors veca=2overset^^i+3overset^^j+4overset^^k, vecb=3overset^^i-overset^^j+2overset^^k "and" vecc=overset^^i+2overset^^j-overset^^k .

Find lambda if the vectors overset^^i-overset^^j+overset^^k,3overset^^i+overset^^j+2overset^^k " and " overset^^i+lambdaoverset^^j-3overset^^k are coplanar.

Show that the vectors 2overset^^i-overset^^j+overset^^k, overset^^i-3overset^^j-5overset^^k and 3overset^^i-4overset^^j-4overset^^k form the vertices of a right angled trainagle.

Find the volume of the following parallelo-piped whose the coterminal edges are: veca=overset^^i-2overset^^j+3overset^^k,vecb=2overset^^i+overset^^j+overset^^k"and" vecc=2overset^^i+overset^^j-overset^^k

Find veca.(vecbxxvecc) ,if veca=2overset^^i+overset^^j+3overset^^k.vecb=-overset^^i+2overset^^j+overset^^k and vecc=3overset^^i+overset^^j+2overset^^k .

Show that the vectors 2overset^^i-3overset^^j+4overset^^k"and " -4overset^^i+6overset^^j-8overset^^k are collinear.

Find [veca" " vecb" " vecc] "if "veca=overset^^i-2overset^^j+overset^^k, vecb=2overset^^i-3overset^^j+overset^^k" and "vecc =3overset^^i+overset^^j-2overset^^k

Let " "veca=overset^^i+4overset^^j+2overset^^k, vecb=3overset^^i-2overset^^j+7overset^^k"and" vecc=2overset^^i-overset^^j+4overset^^k. Find a vector vecd perpendicular to both veca"and"vecb"and"vecc.vecd=15 .

Find the angle between the vectors overset^^i-2overset^^j+3overset^^k"and"3overset^^i-2overset^^j+overset^^k.

Show that the four points with position vectors 4overset^^i+8overset^^j+12overset^^k,2overset^^i+4overset^^j+6overset^^k,3overset^^i+5overset^^j+4overset^^k and 5overset^^i+8overset^^j+5overset^^k are coplanar.

A N EXCEL PUBLICATION-VECTOR ALGEBRA-QUESTION BANK
  1. Area of a rectangle having vertices A,B,C and D with position vectors-...

    Text Solution

    |

  2. Find veca.(vecbxxvecc),if veca=2overset^^i+overset^^j+3overset^^k.vecb...

    Text Solution

    |

  3. Show that the vectors veca=overset^^i-2overset^^j+3overset^^k,vecb=-2...

    Text Solution

    |

  4. Show that the four points A,B,C and D with position cectors 4overset^^...

    Text Solution

    |

  5. Prove that [ veca+vecb vecb+vecc vecc+veca]=2[veca vecb vecc]

    Text Solution

    |

  6. Find the volume of a parallelepiped with coterminal edges represented ...

    Text Solution

    |

  7. Find [veca" " vecb" " vecc] "if "veca=overset^^i-2overset^^j+overset^^...

    Text Solution

    |

  8. Show that the vectors veca=overset^^i-2overset^^j+3overset^^k,vecb=-2...

    Text Solution

    |

  9. Find lambda if the vectors overset^^i-overset^^j+overset^^k,3overset^^...

    Text Solution

    |

  10. Letveca=overset^^i+overset^^j+overset^^k,vecb=overset^^i "and " vecc=c...

    Text Solution

    |

  11. Letveca=overset^^i+overset^^j+overset^^k,vecb=overset^^i "and " vecc=c...

    Text Solution

    |

  12. Show that the four points with position vectors4overset^^i+8overset^^j...

    Text Solution

    |

  13. Find x such that the four points A(3,2,1)B(4,x,5),C(4,2,-2)and D(6,5-1...

    Text Solution

    |

  14. If veca,vecb,veccare coplanar,prove that veca+vecb,vecb+vecc,vecc+veca...

    Text Solution

    |

  15. Find the volume of the following parallelo-piped whose the coterminal ...

    Text Solution

    |

  16. Find the volume of the following parallelo-piped whose the coterminous...

    Text Solution

    |

  17. Find the value of lambdaif the points. A(-1,4,-3),B(3, lamda,-5),C(-3,...

    Text Solution

    |

  18. Write down a unit vector in XY plane making an angle of 30^@ with the...

    Text Solution

    |

  19. Find the scalar components and magnitude of the vector joining the poi...

    Text Solution

    |

  20. A girl walks 4km towards west, then she walks 3 km in a direction 30^@...

    Text Solution

    |