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If a = i + j + k, b = 4i + 3j + 4k, c = ...

If a = i + j + k, b = 4i + 3j + 4k, c = i + `alpha j + beta k` are linearly dependent and `|c| = sqrt(3)` then

A

`alpha =1, beta = - 1`

B

`alpha = 1, beta = +- 1`

C

`alpha = - 1, beta = +- 1`

D

`alpha = +- 1, beta = 1`

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The correct Answer is:
D
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DIPTI PUBLICATION ( AP EAMET)-PRODUCTS OF VECTORS-Exercise 1C (Triple product of Vectors
  1. If the vectors ai + j + k, I + bj + k, I + j + ck (a != b, c != 1) are...

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  2. Let a,b,c the distinct non-negative numbers. If the vectors ai + aj + ...

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  3. If a = i + j + k, b = 4i + 3j + 4k, c = i + alpha j + beta k are linea...

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  4. If the volume of the parallelopiped whose edges are represented by 12i...

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  5. If a = 2i + 3j, b = I + j + k, c = lambda I + 4j + 2k are the edges of...

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  6. If the volume of the parallelopiped with eoterminus edges 4i + 5j + k,...

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  7. The value of k for which the points A (1,0,3), B (-1,3,4) C (1,2,1) an...

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  8. If the points 3i - 2j - k, 2i + 3j - 4k, I + j + 2k, 4i + 5j + lambda ...

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  9. If the volume of the tetrahedron with edges 2i + j -k, I + aj + k and ...

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  10. The volume of the tetrahedron having the edges I + 2j + k, I + j + k, ...

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  11. If a,b,c,d are the position vectors of A,B,C,D respectively then the v...

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  12. If d = x (a xx b) + y (b xx c) + z (c xx a) and [a b c] = 1/8, then x ...

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  13. If a,b,c are non-coplanar vector and lambda is a real number then [lam...

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  14. Let a = I - k,k b - xi + j + (1 - x) k and c = yi + xj + (1 + x - y) k...

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  15. let a be unit vector, b = 2i + j - k and c = I + 3k. The maximum value...

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  16. The vectors a + 2b + 3c, 2a + b - 2c, 3a - 7c are

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  17. The points 2a + 3b - c, a - 2b + 3c, 3a + 4b - 2c, a - 6b + 6c are

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  18. The vectors 5i + 6j + 7k, 7i - 8j + 9k, 3i + 20j + 5k are

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  19. The points (2,1, -1), (1,1,1), (2,2,1), (0,2,5) are

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  20. Let a = 2i + j + k, b = I + 2j - k and a unit vector c be coplanar. If...

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