Home
Class 12
MATHS
Prove that the four points (4hati + 5 ha...

Prove that the four points `(4hati + 5 hatj+hatk), - (hatj +hatk),(3hati+9hatj+4hatk) and 4 (-hati+hatj+hatk)` are coplanar.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • VECTORS

    CBSE COMPLEMENTARY MATERIAL|Exercise TWO MARKS QUESTIONS|11 Videos

  • THREE DIMENSIONAL GEOMETRY

    CBSE COMPLEMENTARY MATERIAL|Exercise SIX MARK QUESTIONS|9 Videos

Similar Questions

Explore conceptually related problems

The value of lamda for which the four points 2hati+3hatj-hatk,hati+2hatj+3hatk,3hati+4hatj-2hatk and hati-lamdahatj+6hatk are coplanar.

Prove that the four points 6 hati - 7hatj, 16hati - 19 hatj - 4hatk, 3hatj - 6hatk and 2hati + 5hatj + 10 hatk form a tetrahedron in spacel.

The value of lambda, for which the four points 2hati+3hatj-hatk, hati-2hatj+3hatk, 3hati+4hatj-2hatk, hati-6hatj+lambda hatk are coplanar, is

Show that the vectors hati-hatj-hatk,2hati+3hatj+hatk and 7hati+3hatj-4hatk are coplanar.

Show that the vectors 4hati-hatj+hatk, 3hati-2hatj-hatk and hati+hatj+2hatk are co-planar.

Find the value of p, if the vectors hati - 2hatj + hatk , 2hati - 5hatj + phatk and 5hati - 9hatj + 4hatk are coplanar .

Find the direction cosines of the resultant of the vectors (hati+hatj+hatk),(-hati+hatj+hatk),(hati-hatj+hatk) and (hati+hatj-hatk) .

CBSE COMPLEMENTARY MATERIAL-VECTORS -FOUR MARKS QUESTIONS
  1. If the vectors vecalpha = a hati + hatj + hatk, vecbeta = hati + b hat...

    Text Solution

    |

  2. Find the altitude of a parallelepiped determined by the vectors veca, ...

    Text Solution

    |

  3. Prove that the four points (4hati + 5 hatj+hatk), - (hatj +hatk),(3hat...

    Text Solution

    |

  4. If |veca| =3, |vecb|=4 and |vecc|=5 such that each is perpendicular to...

    Text Solution

    |

  5. Decompose the vector 6 hati - 3 hatj - 6 hatk into vectors which are p...

    Text Solution

    |

  6. If veca, vecb and vecc are vectors such that veca. vecb = veca.vecc, v...

    Text Solution

    |

  7. If veca, vecb and vecc are three non zero vectors such that veca xx v...

    Text Solution

    |

  8. For any three vectors veca, vecb, vecc the value of [(veca-vecb, vecb-...

    Text Solution

    |

  9. If [veca vecbvecc]=2 find the volume of the parallelepiped whose co-te...

    Text Solution

    |

  10. If veca +vecb +vecc=0, |veca|=3,|vecb|=5, |vecc|=7 , then find the ang...

    Text Solution

    |

  11. If the magnitude of the vector product of the vector hati+hatj+hatk wi...

    Text Solution

    |

  12. If vecaxxvecb=veccxxvecd and vecaxxvecc=vecbxxvecd show that (veca-vec...

    Text Solution

    |

  13. Find a vector of magnittude sqrt(171) which is perpendicular to both o...

    Text Solution

    |

  14. If a is a nonzero real number prove that the vectors overset(r) alph...

    Text Solution

    |

  15. If with reference to a right handed system of mutually perpendicula...

    Text Solution

    |

  16. Find a unit vector perpendicular to plane ABC when position vectors of...

    Text Solution

    |

  17. Find a unit vector in XY plane which makes an angle 45^(@) with the ve...

    Text Solution

    |

  18. Suppose veca = lamda hati - 7 hatj + 3 hatk, vecb = lamda hati + hatj ...

    Text Solution

    |

  19. Let vecV = 2hati +hatj - hatk and vecW= hati + 3hatk . if vecU is a u...

    Text Solution

    |

  20. Let veca=hati-hatk, vecb=xhati+hatj+(1-x)hatk and vecc=yhati+xhatj+(1+...

    Text Solution

    |