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A vector a has components 2p and 1 with...

A vector a has components 2p and 1 with respect to a rectangular cartesian system. This system is rotated through a certain angle about the origin in the counter-clockwise sense. If with respect to new system, a has components `p +1` and 1, then

A

`p =0`

B

`p = 1 or p = -(1)/(3)`

C

`p = -1 or p = (1)/(3)`

D

`p = 1 or p =-1`

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The correct Answer is:
B
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ML KHANNA-ADDITION AND MULTIPLICATION OF VECTORS -Self Assessment Test (MULTIPLE CHOICE QUESTIONS)
  1. If A = 2i + 2j-k, B = 6i-3j+2k, then A xx B will be given by

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  2. The number of vectors of unit length perpendicular to vectors vec ...

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  3. A vector a has components 2p and 1 with respect to a rectangular cart...

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  4. If |vecalpha + vecbeta| = |vecalpha - vecbeta|, then

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  5. If veca and vecb are two vectors such that veca.vecb = 0 and veca xx v...

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  6. Let veca, vecb, vecc be three non-coplanar vectors and vecp,vecq,vecr ...

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  7. The components of a vector veca along and perpendicular to a non-zero ...

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  8. For any three vectors a, b, c (a-b).{(b-c) xx (c-a)} = 2a.(bxxc). ...

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  9. If a = 4i + 6j and b = 3j+4k, then the vector form of component of a a...

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  10. A unit vector perpendicular to the vector 4i-j+3k and -2i+j-2k is

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  11. The unit vector perpendicular to the two vectors i-j and i+2j, and per...

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  12. If u = i xx (a xx i), + j xx (a xx j) + k xx(a xx k), then

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  13. The volume of a parallelopiped whose sides are given by vecOA =2i-3j,v...

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  14. If alpha = 2i + 3j - k, beta = -i + 2j-4k, gamma = i+j+k then the valu...

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  15. Let vec a=2 hat i- hat j+ hat k , vec b= hat i+2 hat j= hat ka n d ve...

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  16. If the vectors vec c , vec a=x hat i+y hat j+z hat ka n d vec b= hat ...

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  17. If veca lies in the plane of vectors vecb and vecc, then which of the ...

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  18. If a xx b = c, b xx c = a and a, b,c be moduli of the vectors a, b,c...

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  19. Let a-i+j and b=2i-k.The point of intersection of the lines r times a=...

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  20. Let a,b, c be three non-coplanar vectors and r be any vector in space ...

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