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Let P and Q are two points on curve `y=log_((1)/(2))(x-(1)/(2))+log_(2) sqrt(4x^(2)-4x+1)` and P is also on `x^(2)+y^(2)=10`. Q lies inside the given circle such that its abscissa is integer. Find the smallest possible value of `vec(OP)*vec(OQ)` where 'O' being origin.

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VIKAS GUPTA (BLACK BOOK)-VECTOR & 3DIMENSIONAL GEOMETRY-Exercise-5 : Subjective Type Problems
  1. A straight line L intersects perpendicularly both the lines : (x+2)/...

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

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  3. Let OA, OB, OC be coterminous edges of a cubboid. If l, m, n be the sh...

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

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  5. Let vec v(0) be a fixed vector and vecv(0)=[(1)/(0)]. Then for n ge ...

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

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

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

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

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  10. The plane denoted by P(1) : 4x+7y+4z+81=0 is rotated through a right a...

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

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

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

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

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  15. Let P and Q are two points on curve y=log((1)/(2))(x-(1)/(2))+log(2) s...

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  16. Let P and Q are two points on curve y=log((1)/(2))(x-(1)/(2))+log(2) s...

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

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