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The plane denoted by `P_1 : 4x+7y+4z+81=0` is rotated through a right angle about its line of intersection with plane `P_2 : 5x+3y+10z=25`. If the plane in its new position be denoted by P, and the distance of this plane from the origin is d, then the value of `[(k)/(2)]` (where[.] represents greatest integer less than or equal to k) is....

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VIKAS GUPTA (BLACK BOOK) ENGLISH-VECTOR & 3DIMENSIONAL GEOMETRY-Exercise-5 : Subjective Type Problems
  1. A rod AB of length 2L and mass m is lying on a horizontal frictionless...

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  2. If hata, hatb and hatc are non-coplanar unti vectors such that [hata ...

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  3. Let OABC be a tetrahedron whose edges are of unit length. If vec OA = ...

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  4. If A is the matrix [(1,-3),(-1,1)], then A-(1)/(3)A^(2)+(1)/(9)A^(3)……...

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  5. A sequence of 2xx2 matrices {M(n)} is defined as follows M(n)=[((1)/(...

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  6. Let |veca|=1, |vecb|=1 and |veca+vecb|=sqrt(3). If vec c be a vector ...

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  7. Let vecr=(veca xx vecb)sinx+(vecb xx vec c)cosy+2(vec c xx vec a), whe...

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  8. The plane denoted by P1 : 4x+7y+4z+81=0 is rotated through a right ang...

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  9. ABCD is a regular tetrahedron, A is the origin and B lies on x-axis. A...

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  10. A, B, C, D are four points in the space and satisfy |vec(AB)|=3, |vec(...

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  11. Let OABC be a regular tetrahedron of edge length unity. Its volume be ...

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  12. If veca and vecb are non zero, non collinear vectors and veca(1)=lamb...

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  13. Let P and Q are two points on the curve y=log((1)/(2))(x-0.5)+log2sqrt...

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  14. Let P and Q are two points on the curve y=log((1)/(2))(x-0.5)+log2sqrt...

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  15. If a, b, c, l, m, n in R-{0} such that al+bm+cn=0, bl+cm+an=0, cl+am+b...

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  16. Let vec ua n d vec v be unit vectors such that vec uxx vec v+ vec u=...

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