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The volume of a parallelepiped with edge...

The volume of a parallelepiped with edges `vec(OA)=(3,1.4),vec(OB)=(1,2,3),vec(OC)=(2,1,5)` is ……………

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If one of the vertices of a parallelopiped is origin and its edges are bar(OA),bar(OB) and bar(OC) where where A(4, 3, 1), B(3, 1, 2) and C(5, 2, 1), then find the volume of this parallelopiped.

Orthocenter of an equilateral triangle ABC is the origin O. If vec(OA)=veca, vec(OB)=vecb, vec(OC)=vecc , then vec(AB)+2vec(BC)+3vec(CA)=

Knowledge Check

  • Let vec(a),vec(b) and vec( c ) are three unit vectors such that vec(a)xx(vec(b)xx vec( c ))=(sqrt(3))/(2)(vec(b)+vec( c )) . If the vectors vec(b) and vec( c ) are not parallel then the angle between vec(a) and vec(b) is ……….

    A
    `(3pi)/(4)`
    B
    `(pi)/(2)`
    C
    `(2pi)/(3)`
    D
    `(5pi)/(6)`

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    Find a vector of magnitude sqrt(51) and makes equal angle with the vectors vec(a)=(1)/(3)(hati-2hatj+2hatk),vec(b)=(1)/(5)(-4hati-3hatk) and vec( c )=hatj .

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    Statement -1 : If a transversal cuts the sides OL, OM and diagonal ON of a parallelogram at A, B, C respectively, then (OL)/(OA) + (OM)/(OB) =(ON)/(OC) Statement -2 : Three points with position vectors veca , vec b , vec c are collinear iff there exist scalars x, y, z not all zero such that x vec a + y vec b +z vec c = vec 0, " where " x +y + z=0.

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