Home
Class 12
MATHS
Area of a rectangle having vertices : A(...

Area of a rectangle having vertices : `A(-hati+1/2 hatj+4hatk),B(hati+1/2hatj+4hatk),C(hati-1/2 hatj+4hatk),D(-hati-1/2hatj+4hatk)` is :

A

`1/2`

B

1

C

2

D

4

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • VECTOR ALGEBRA

    OMEGA PUBLICATION|Exercise IMPORTANT QUESTION FROM MISCELLANEOUS EXERCISE |10 Videos

  • THREE DIMENSIONAL GEOMETRY

    OMEGA PUBLICATION|Exercise Questions |72 Videos

Similar Questions

Explore conceptually related problems

Area of a rectangle having vertices A, B, C and D with position vectors : -hati + (1/2)hatj + 4hatk, hati + (1/2)hatj + 4hatk, hati - (1/2)hatj + 4hatk and -hati - (1/2)hatj + 4hatk , respectively is:

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

Determine whether or not the following pairs of lines intersect : vecr=(hati-2hatj+3hatk)+lambda(-hati+hatj-2hatk) and vecr=(hati-hatj-hatk)+mu(hati+2hatj-2hatk)

If a=3hati-2hatj+hatk,b=2hati-4hatj-3hatk and c=-hati+2hatj+2hatk , then a+b+c is

Consider the equation of the straight lines given by : L_1:vecr=(hati+2hatj+hatk)+lambda(hati-hatj+hatk) L_2:vecr=(2hati-hatj-hatk)+mu(2hati+hatj+2hatk) If veca_1=hati+2hatj+hatk, vecb_1=hati-hatj+hatk, veca_2=2hati-hatj-hatk, vecb_2=2hati+hatj+2hatk , then find : (vecb_1xxvecb_2)*(veca_2-veca_1)

Consider the equation of the straight lines given by : L_1:vecr=(hati+2hatj+hatk)+lambda(hati-hatj+hatk) L_2:vecr=(2hati-hatj-hatk)+mu(2hati+hatj+2hatk) If veca_1=hati+2hatj+hatk, vecb_1=hati-hatj+hatk, veca_2=2hati-hatj-hatk, vecb_2=2hati+hatj+2hatk , then find : veca_2-veca_1

Consider the equation of the straight lines given by : L_1:vecr=(hati+2hatj+hatk)+lambda(hati-hatj+hatk) L_2:vecr=(2hati-hatj-hatk)+mu(2hati+hatj+2hatk) If veca_1=hati+2hatj+hatk, vecb_1=hati-hatj+hatk, veca_2=2hati-hatj-hatk, vecb_2=2hati+hatj+2hatk , then find : vecb_2-vecb_1

Consider the equation of the straight lines given by : L_1:vecr=(hati+2hatj+hatk)+lambda(hati-hatj+hatk) L_2:vecr=(2hati-hatj-hatk)+mu(2hati+hatj+2hatk) If veca_1=hati+2hatj+hatk, vecb_1=hati-hatj+hatk, veca_2=2hati-hatj-hatk, vecb_2=2hati+hatj+2hatk , then find : vecb_1xxvecb_2

Consider the equation of the straight lines given by : L_1:vecr=(hati+2hatj+hatk)+lambda(hati-hatj+hatk) L_2:vecr=(2hati-hatj-hatk)+mu(2hati+hatj+2hatk) If veca_1=hati+2hatj+hatk, vecb_1=hati-hatj+hatk, veca_2=2hati-hatj-hatk, vecb_2=2hati+hatj+2hatk , then find : veca_1xxveca_2

OMEGA PUBLICATION-VECTOR ALGEBRA -MULTIPLE CHOICE QUESTIONS (MCQs)
  1. If a is a non-zero vector of magnitude V a is a non-zero scalar, then ...

    Text Solution

    |

  2. Let the vectors veca and vecb be such that |veca|=3 and |vecb|=(sqrt2)...

    Text Solution

    |

  3. Area of a rectangle having vertices : A(-hati+1/2 hatj+4hatk),B(hati+1...

    Text Solution

    |

  4. If theta is the angle between two vectors veca and vecb, then veca c...

    Text Solution

    |

  5. Let veca and vecb be two unit vectors and theta is the angle between t...

    Text Solution

    |

  6. If (hati,hatj,hatk) are the usual three perpendicular unit vectors, th...

    Text Solution

    |

  7. Using vectors, find the area of the triangle having vertices A (1, 1, ...

    Text Solution

    |

  8. the angle between vectors veca × vecb and vecb × veca is

    Text Solution

    |

  9. Show that the area of the parallelogram with diagonals veca and vecb, ...

    Text Solution

    |

  10. The area of triangle having adjacent sides veca and vecb is :

    Text Solution

    |

  11. The value of : hati*(hatjxxhatk)+hatj*(hatixxhatk)+hatk*(hatixxhatj) i...

    Text Solution

    |

  12. If theta is the angle between two vectors veca and vecb, then |veca*ve...

    Text Solution

    |

  13. If veca*vecb=-|veca||vecb|, then theta=

    Text Solution

    |

  14. The projection of the vector veca=2hati+3hatj+2hatk on the vector vecb...

    Text Solution

    |

  15. The product of veca.vecb equals to:

    Text Solution

    |

  16. The product of veca.vecb equals to:

    Text Solution

    |

  17. The vectors a and b are perpendicular, if

    Text Solution

    |

  18. If veca xx vecb=|veca||vecb| sin theta hatn which one is correct

    Text Solution

    |

  19. Find the angle between two vectors vecaand vecb with magnitudes 1 and ...

    Text Solution

    |

  20. Find the angle between the vectors : veca=hati+hatj-hatk and vecb=hati...

    Text Solution

    |