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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 -Problem Set (2) (MULTIPLE CHOICE QUESTIONS)
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  2. If |a| = |b|, then (a +b). (a-b) is

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

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  4. Let a =i+j+pk and b=i+j+k, |a+b| =|a| +|b| , holds for

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  5. If x and y are two unit vectors and phi is the angle between them, the...

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  6. Let hat(a), hat(b) be two unit vectors and theta be the angle between...

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  7. (a +b). (a-b) =0 implies that

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  8. The vectors vec A and vec B are such that |vec A + vec B | = |vec A - ...

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  9. (a + b) xx (a-b) is equal to

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  10. If u = a-b, v =a + b and |a| = |b| = 2, then |u xx v| is

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  11. Let vec aa n d vec b be two non-collinear unit vector. If vec u= vec...

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  12. If \ vec a\ a n d\ vec b are two unit vectors inclined at an angle t...

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  13. If veca and vecb are two unit vectors such that veca+2vecb and 5veca-4...

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  14. The vector a + 3b is perpendicular to 7a-5b and a-5b is perpendicular ...

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  15. Four points with position vectors 7i-4j+7k, i -6j+10k,-i-3j+4k and 5i-...

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  16. a, b, c, d are the vertices of a square, then

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  17. ai + 3j + 4k and sqrt(b) i+5k are two vectors, where a, b gt 0 are tw...

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  18. A parallelogram is constructed on the vectors r(1) = 3a-b, r(2) = a + ...

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  19. The vectors a =3i-2j+2k and b =-i-2k are adjacement sides of a parall...

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  20. The length of longer diagonal of the parallelogram constructed on 5...

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