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Let B1,C1 and D1 are points on AB,AC and...

Let `B_1,C_1 and D_1` are points on `AB,AC and AD` of the parallelogram `ABCD,` such that `vec(AB_1)=k_1vec(AC,) vec(AC_1)=k_2vec(AC) and vec(AD_1)=k_2 vec(AD,)` where `k_1,k_2 and k_3` are scalar.

A

`lambda_(1), lambda_(3) and lambda_(2) ` are in AP

B

`lambda_(1), lambda_(3) and lambda_(2)` are in GP

C

`lambda_(1),lambda_(3) and lambda_(2)` are in HP

D

`lambda_(1)+lambda_(2)+lambda_(3)=0`

Text Solution

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The correct Answer is:
C
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VIKAS GUPTA (BLACK BOOK)-VECTOR & 3DIMENSIONAL GEOMETRY-Exercise-5 : Subjective Type Problems
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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 P(1) : 4x+7y+4z+81=0 is rotated through a right a...

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

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

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

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

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

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