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Let ` vec a , vec ba n d vec c` be three non-coplanar vecrors and ` vec r` be any arbitrary vector. Then `( vec axx vec b)xx( vec rxx vec c)+( vec bxx vec c)xx( vec rxx vec a)+( vec cxx vec a)xx( vec rxx vec b)` is always equal to `[ vec a vec b vec c] vec r` b. `2[ vec a vec b vec c] vec r` c. `3[ vec a vec b vec c] vec r` d. none of these

A

`[veca vecb vec c]vecr`

B

`2[veca vecb vec c]vecr`

C

`4[veca vecb vec c]vecr`

D

`vec0`

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The correct Answer is:
B
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VK JAISWAL-VECTOR & 3DIMENSIONAL GEOMETRY-Exercise-5 : Subjective Type Problems
  1. Let vec a , vec ba n d vec c be three non-coplanar vecrors and ve...

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  2. A straight line L intersects perpendicularly both the lines : (x+2)/...

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

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

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

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

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

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

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

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

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

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

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

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

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  15. In above problem find the largest possible value of |vec(PQ)|.

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

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