Home
Class 12
MATHS
Show that area of the parallelogram whos...

Show that area of the parallelogram whose diagonals are given by `vec(a)` and `vec(b)` is `(1)/(2).|bar(a)xx bar(b)|`. Also, find the area of the parallelogram, whose diagonals are `2 bar(i)-bar(j)+bar(k)` and `bar(i)+3bar(j)-bar(k)`.

Text Solution

Verified by Experts

The correct Answer is:
`=(1)/(2)(sqrt(62))` sq. unit
Promotional Banner

Topper's Solved these Questions

  • VECTOR ALGEBRA

    KUMAR PRAKASHAN|Exercise Solutions of NCERT Exemplar Problems (Objective type Questions)|23 Videos

  • VECTOR ALGEBRA

    KUMAR PRAKASHAN|Exercise Solutions of NCERT Exemplar Problems (True/False)|5 Videos

  • VECTOR ALGEBRA

    KUMAR PRAKASHAN|Exercise Textbook Illustrations for Practive Work|36 Videos

  • THREE DIMENSIONAL GEOMETRY

    KUMAR PRAKASHAN|Exercise PRACTICE PAPER -11|16 Videos

Similar Questions

Explore conceptually related problems

Find a vector of magnitude 6, which is perpendicualr to both the vectors 2bar(i)-bar(j)+2bar(k) and 4bar(i)-bar(j)+3bar(k) .

The number of vectors of unit length perpendicular to the vectors bar(a)=2bar(i)+bar(j)+2bar(k) and bar(b)=bar(j)+bar(k) is ………….

[bar(a)xx bar(b)" "bar(a)xx bar( c )" "bar(d)] = …………….

(bar(a)xx bar(b))^(2) = ……………..

Find the distance between the planes bar(r) * ( 2 bar(i) - bar(j) + 3 bar(k)) = 4 and bar(r) * ( 6 bar(i) - 3 bar(j) + 9 bar(k)) + 13 = 0

The value of lambda for which the vectors 3bar(i)-6bar(j)+bar(k) and 2bar(i)-4bar(j)+lambda bar(k) are parallel is …..

bar(a)=hati+hatj+hatk,bar(b)=hati+3hatj+5hatk and bar( c )=7hati+9hatj+11hatk are vectors. The area of the parallelogram whose diagonals are bar(a)+bar(b) and bar(b)+bar( c ) is …………..

ABCD is a parallelogram whose diagonals meet at P. If O is a fixed point, then bar(OA)+bar(OB)+bar(OC)+bar(OD) equals :

|bar(a)|=2,|bar(b)|=3 and bar(a) and bar(b) are perpendicular to each other. The area of the triangle with vertices bar(0),bar(a)+bar(b) and bar(a)-bar(b) is ……………

If |bar(a)+bar(b)|=|bar(a)-bar(b)| , then the vectors bar(a) and bar(b) are orthogonal.

KUMAR PRAKASHAN-VECTOR ALGEBRA -Solutions of NCERT Exemplar Problems (Short Answer Type Questions)
  1. Find the unit vector in the direction of sum of vectors vec(a)=2hati-h...

    Text Solution

    |

  2. If bar(a)=hati+hatj+2hatk and bar(b)=2hati+hatj-2hatk, find the unit v...

    Text Solution

    |

  3. Find a unit vector in the direction of vec(PQ), where P and Q have coo...

    Text Solution

    |

  4. If A and B are the positon vectors of bar(a) and bar(b) respectively, ...

    Text Solution

    |

  5. Using vectors, find the value of k, such that the points (k,-10,3),(1,...

    Text Solution

    |

  6. A vector bar( r ) is inclined at equal angles to the three axes. If th...

    Text Solution

    |

  7. If a vector vec( r ) has magnitude 14 and direction ratios 2, 3, -6. T...

    Text Solution

    |

  8. Find a vector of magnitude 6, which is perpendicualr to both the vecto...

    Text Solution

    |

  9. Find the angle between the vectors 2hati-hatj+hatk and 3hati+4hatj-hat...

    Text Solution

    |

  10. If bar(a)+bar(b)+bar( c )=0, then show that bar(a)xx bar(b)=bar(b)xx b...

    Text Solution

    |

  11. Find the sine of the angle between the vectors bar(a)=3hati+hatj+2hatk...

    Text Solution

    |

  12. If A, B, C and D are the points with position vectors hati+hatj-hatk,2...

    Text Solution

    |

  13. Using vectors, find the area of the DeltaABC with vertices A(1,2,3),B(...

    Text Solution

    |

  14. Using vectors, prove that the parallelogram on the same base and betwe...

    Text Solution

    |

  15. Prove that in any DeltaABC,cos A=(b^(2)+c^(2)-a^(2))/(2bc) where a, ...

    Text Solution

    |

  16. Show that area of the parallelogram whose diagonals are given by vec(a...

    Text Solution

    |

  17. If bar(a)=bar(i)+bar(j)+bar(k) and bar(b)=bar(j)-bar(k), then find a v...

    Text Solution

    |