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Conside the matrices A=[(1,2,3),(4,1,2),...

Conside the matrices `A=[(1,2,3),(4,1,2),(1,-1,1)]` `B=[(2,1,3),(4,1,-1), (2,2,3)]` `C=[(14),(12),(2)]` `D=[(13),(11),(14)]`. Now `x=[(x),(y),(z)]`is such that solutions of equation `AX=C` and `BX=D` represent two points L andM respectively in 3 dimensional space. If `L'` and `M'` are hre reflections of L and M in the plane x+y+z=9 then find coordinates of L,M,L',M'

A

(3, 4, 2)

B

(5, 3, 4)

C

(7, 2, 3)

D

(1, 5, 6)

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VK JAISWAL-VECTOR & 3DIMENSIONAL GEOMETRY-Exercise-5 : Subjective Type Problems
  1. Conside the matrices A=[(1,2,3),(4,1,2),(1,-1,1)] B=[(2,1,3),(4,1,-1),...

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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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