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If bar(a), bar(b), bar(c ) respresents ...

If `bar(a), bar(b), bar(c )` respresents the vertices A, B, and C respectively of `DeltaABC` then prove that `|(bar(a) xx bar(b)) + (bar(b) xx bar(c ))+ (bar(c ) xx bar(a))|` is twice the area of `DeltaABC`.

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Explore conceptually related problems

If A,B, C and D are four points, then show that |bar(AB) xx bar(CD) + bar(BC) xx bar(AD) + bar(CA) xx bar(BD)| is four times the area of Delta ABC

If bar(a)+bar(b)+bar(c)=bar(0) then prove that bar(a)xxbar(b)=bar(b)xxbar(c)=bar(c)xxbar(a) .

Knowledge Check

  • If A,B,C,D are four point and |bar(AB) xx bar(CD) +bar(BC)xx bar(AD) +bar(CA) xx bar(BD)| = k ("Area of "DeltaABC) , then k =

    A
    1
    B
    2
    C
    3
    D
    4

  • The angle between (bar(A) xx bar(B)) and (bar(B) xx bar(A)) is (in radiant)

    A
    `pi//2`
    B
    `pi`
    C
    `pi//4`
    D
    zero

    • Similar Questions

    Explore conceptually related problems

    Find bar(a) xx (bar(b) + bar(c )) + bar(b) xx (bar(c ) + bar(a)) + bar(c ) xx (bar(a) + bar(b))

    Compute bar(a) xx (bar(b) + bar(c )) + bar(b) xx (bar(c ) +bar(a)) + bar(c ) xx (bar(a)+bar(b))

    Show that (bar(a)+bar(b)) . [(bar(b)+bar(c)) xx (bar(c )+bar(a))] = 2[bar(a)bar(b)bar(c )] .

    If bar(a), bar(b), bar(c ) are P.V's of the vertices A,B,C respectively of DeltaABC then find the vector equation of the median through the vertex A.

    If bar(a), bar(b), bar(c) are the position vectors of the vertices A, B, C respectively of DeltaABC then find the vector equation of the median through the vertex A.

    In Delta ABC, if bar(a), bar(b), bar(c) are position vectors of the vertices A, B, and C respectively, then prove that the position vector of the centroid G is (1)/(3) (bar(a) + bar(b) + bar(c))

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