Home
Class 12
MATHS
Check whether the given three vectors ar...

Check whether the given three vectors are coplnar or non- coplanar :
`-2hati -2 hatj + 4hatk, -2hati + 4hatj -2hatk, 4hati - 2hatj - 2hatk`.

Text Solution

Verified by Experts

Given vectors are `-2hati -2hatj +4hatk, -2hati +4hatj -2hatk, 4hati -2hatj -2hatk`
`rArr " " |{:(-2,,-2,,4),(-2,,4,,-2),(4,,-2,,-2):}| = 16 + 16 + 16 - 64 + 8 +8 =0`
Hence, the vectors are coplanar.
Promotional Banner

Topper's Solved these Questions

  • INTRODUCTION TO VECTORS

    CENGAGE|Exercise Exercise 1.1|20 Videos
  • INTRODUCTION TO VECTORS

    CENGAGE|Exercise Exercise 1.2|7 Videos
  • INTEGRALS

    CENGAGE|Exercise Solved Examples And Exercises|324 Videos
  • INVERSE TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Question Bank|24 Videos

Similar Questions

Explore conceptually related problems

Find the vector equation of the plane passing through the point hati + hatj -2hatk and hati + 2hatj + hatk, 2hati - hatj + hatk.

Fina a unit vector in the direaction of the resultant of the vectors hati - hatj + 3hatk, 2 hati + hatj- 2 hatk and hati + 2 hatj- 2 hatk.

The vectors lambdahati + hatj + 2hatk, hati + lambdahatj +hatk, 2hati - hatj + 2hatk are coplanar, if:

A vector coplanar with vectores hati + hatj and hatj + hatk and parallel to the vector 2 hati - 2 hatj - 4 hatk is

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

A unit vector perpendicular to both the vectors 2hati-2hatj+hatk and 3hati+4hatj-5hatk , is

Find the volume of the parallelopiped, if the coterminus edges are given by the vectors 2hati + 5hatj - 4hatk . 5hati + 7hatj + 5hatk , 4hati + 5hatj - 2hatk

The area of the triangle having vertices as hati-2hatj+3hatk,-2hati+3hatj-hatk,4hati-7hatj+7hatk is

CENGAGE-INTRODUCTION TO VECTORS -JEE Previous Year
  1. Check whether the given three vectors are coplnar or non- coplanar : ...

    Text Solution

    |

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

    Text Solution

    |

  3. A vector a has components a1,a2,a3 in a right handed rectangular cart...

    Text Solution

    |

  4. The position vectors of the point A, B, C and D are 3hati-2hatj -hatk,...

    Text Solution

    |

  5. Let O A C B be a parallelogram with O at the origin andO C a diagonal....

    Text Solution

    |

  6. In a triangle A B C ,Da n dE are points on B Ca n dA C , respectivley,...

    Text Solution

    |

  7. Prove, by vector method or otherwise, that the point of intersectio...

    Text Solution

    |

  8. Show, by vector methods, that the angularbisectors of a triangle are c...

    Text Solution

    |

  9. Let A(t)=f1(t)veci+f2(t)vecj and vecB(t)=g1(t)veci+g2(t)vecj, tepsilon...

    Text Solution

    |

  10. In a triangle OAB,E is the mid point of OB and D is the point on AB s...

    Text Solution

    |

  11. If |{:(a,,a^(2),,1+a^(3)),(b,,b^(2),,1+b^(3)),(c,,c^(2),,1+c^(3)):}|=0...

    Text Solution

    |

  12. If the vectors ahati+hatj+hatk, hati+bhatj+hatk, hati+hatj+chatk(a!=1,...

    Text Solution

    |

  13. The points with position vectors veca + vecb, veca-vecb and veca +k ve...

    Text Solution

    |

  14. The points with position vectors 60hati+3hatj,40hati-8hatj, 40hati-8ha...

    Text Solution

    |

  15. Let a, b and c be distinct non-negative numbers. If vectos a hati +a h...

    Text Solution

    |

  16. Let veca =veci -veck, vecb = xveci+ vecj + (1-x)veck and vecc =y veci ...

    Text Solution

    |

  17. Let alpha, beta, gamma be distinct real numbers. The points with posit...

    Text Solution

    |

  18. The number of distinct values of lamda, for which the vectors -lamda^(...

    Text Solution

    |

  19. If veca=hati+hatj+hatk, vecb=4hati+3hatj+4hatk and vecc=hati+alphahatj...

    Text Solution

    |

  20. Consider the set of eight vector V={a hat i+b hat j+c hat k ; a ,bc in...

    Text Solution

    |

  21. Suppose that vecp, vecq and vecr are three non-coplanar vectors in R^...

    Text Solution

    |