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

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

A

`alpha =1, beta =-1`

B

`alpha =1, beta = pm1`

C

`alpha =-1,beta=pm1`

D

`alpha =pm1,beta =1`

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The correct Answer is:
D
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ML KHANNA-ADDITION AND MULTIPLICATION OF VECTORS -Problem Set (3) (MULTIPLE CHOICE QUESTIONS)
  1. If a,b,c be three non-coplanar vectors, then (i) [a-b,b-c,c-a]=

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  2. If A, B, C are three points with position vectors i+j,i-j and p.i+qj+...

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  3. If a = i +j + k, b = 4i + 3j + 4k and c = i + alphaj + betak are linea...

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  4. If a.b = b.c = c.a = 0, then a.(bxxc)=

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  5. For non-coplanar vectors a, b and c, abs((a times b)*c)=abs(a) abs(b) ...

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  6. If x=3i-6j-k, y=i+4j-3k" and "z=3i-4j-12k, then the magnitude of the p...

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  7. IF a,b,c are non-coplanar vectors, then |{:(a.a,,a.b.,,a.c),(b.a,,b....

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  8. a,b,c are unit vectors such that aand b are mutualy perpendicular and ...

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  9. If a,b and c are three non-coplanar vectors, then the scalar product o...

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  10. If a, b and c are non-zero vectors such that a times b=c, b times c=a ...

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  11. a =2i-j+k, b=i+2j-3k, c=3i+lambdaj+5k and if these vectors be coplanar...

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  12. The position vectors of the points A,B,C,D are vec(3i)-vec(2j)-veck, v...

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  13. The value of lambda for which the points L(1,0,3), M(-1,3,4),N(1,2,1) ...

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

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  15. IF r.a = 0, r. b = 0 and r. c= 0 for some non-zero vector r. Then, the...

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  16. If a, b,c are non-coplanar vectors such that r.a = r.b = r.c =0, then

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  17. Blank,

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  18. If |[a, b, c], [a^(2), b^(2), c^(2)], [a^(3)+1, b^(3)+1, c^(2)+1]|=0 a...

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  19. If the vectors ai + j + k , i + bj + k and i + j + ck, where a, b, c n...

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  20. Another form (1+a)/(1-a) + (1+b)/(1-b) + (1 +c)/(1-c) =

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