Home
Class 11
MATHS
Show that the vector area of the quadril...

Show that the vector area of the quadrilateral ABCD having diagonals `vec(AC),vec(BD)` is `1/2(vec(AC)xxvec(BD))`.

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(2)(vec(AC)xxvec(BD))`.
Promotional Banner

Topper's Solved these Questions

  • PRODUCT OF VECTORS

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise EXERCISE 5(c) III|11 Videos

  • PAIR OF STRAIGHT LINES

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise EXERCISE - 4(c) III. |3 Videos

  • PROPERTIES OF TRIANGLES

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise TEXTUAL EXERCISES ( EXERCISE - 10(b) ) III.|11 Videos

Similar Questions

Explore conceptually related problems

The vector area of the parallelogram whose diagonals are vec(i) + 2vec(j) + 3vec(k), -vec(i) - 2vec(j) + vec(k) is

The vector area of the parallelogram whose adjacent sides vec(i) + vec(j) + vec(k) and 2vec(i)-vec(j) + 2vec(k) is

The vector area of the triangle formed by the points vec(i) -vec(j) + vec(k), 2vec(i) + vec(j) -2vec(k) and 3vec(i) + vec(j) + 2vec(k) is

Let vec(OA)= vec(a), vec(OB)= 10vec(a) + 2vec(b), vec(OC )= vec(b) where O, A, C are non-collinear points. Let lamda denote the area of the quadrilateral OABC and let mu denote the area of parallelogram with vec(OA) and vec(OC) as ajacent sides show that lamda= 6mu

In a rectangle ABCD, the diagonal AC= 10cm then diagonal BD= ………cm.

In the parallelogram ABCD, overline(AC)^(2)- overline(BD)^(2) =

For any vector vec(a) , the value of (vec(a) xx vec(i))^(2) + (vec(a) xx vec(j))^(2) + (vec(a) xx vec(k))^(2)=

If |vec(a)|=sqrt3, |vec(b)|=2, (vec(a), vec(b))= (pi)/(3) , then the area of the triangle with adjacent sides vec(a) + 2vec(b) and 2vec(a) + vec(b) (in sq.u) is

VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-PRODUCT OF VECTORS-SOLVED PROBLEMS
  1. A non-zero vector bar(a), is parallel to the line of intersection of t...

    Text Solution

    |

  2. If vec(a)= 4vec(i) + 5vec(j)- vec(k), vec(b)= vec(i)- 4vec(j) + 5vec(k...

    Text Solution

    |

  3. For any vector bar(a) show that |bar(a) xx bar(i)|^(2) + |bar(a) xx ba...

    Text Solution

    |

  4. If veca is non-zero vector and b,vec(c) are two vector such that vecax...

    Text Solution

    |

  5. Prove that the vectors vec(a)=2veci-vecj+veck,vecb=veci-3vecj-5veck an...

    Text Solution

    |

  6. Find the volume of the parallelopiped having co-tenninus edges are rep...

    Text Solution

    |

  7. If the vectors veca=2veci-vecj+veck,vecb=veci+2vecj-3veck and vecc=3ve...

    Text Solution

    |

  8. Show that vecixx(vecaxxveci)+vecjxx(vecaxxvecj)+kxx(vecaxxveck)=2veca ...

    Text Solution

    |

  9. Prove that for any three vectors veca,vecb,vec(c),[b+c" "c+a" "a+b]=2[...

    Text Solution

    |

  10. For any three vectors veca,vecb,vec(c) prove that [vecbxxvec(c)" "vec(...

    Text Solution

    |

  11. If a,b,c are three unit vectors such that a xx (b xx c) = (1)/(2) b th...

    Text Solution

    |

  12. Find the equation of the plane passing through the point A=(2,3,-1),B=...

    Text Solution

    |

  13. Find the equation of the plane passing through the point A=(3,-2,-1) a...

    Text Solution

    |

  14. Find the vector equation of the plane passing through the intersection...

    Text Solution

    |

  15. Find the distance of a point (2,5,-3) from the planer r.(6i-3j+2k)=4

    Text Solution

    |

  16. Find the angle between line (x+1)/2 = y/3 = (z-3)/6 and the plane 10x ...

    Text Solution

    |

  17. For any four vectors a,b,c and d, (axxb)xx(cxxd)=["a c d"]b-["b c d"]a...

    Text Solution

    |

  18. Find the shortest distance between the skew lines . bar(r)=(6bar(i)...

    Text Solution

    |

  19. Prove that angle in a semi circle is a rightangle by using Vector meth...

    Text Solution

    |

  20. Show that the vector area of the quadrilateral ABCD having diagonals v...

    Text Solution

    |