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Let a,b,c be distinct non-negative numbe...

Let `a,b,c` be distinct non-negative numbers. If the vectors `ahati+ahatj+chatk, hati+hatk` and `chati+chatj+bhatk` lies in a plane then `c` is

A

the Arithmetic Mean of a and b

B

the Geometric Mean of a and b

C

the Harmonic Mean of a and b

D

equal to zero

Text Solution

Verified by Experts

The correct Answer is:
B
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ML KHANNA-ADDITION AND MULTIPLICATION OF VECTORS -Problem Set (3) (MULTIPLE CHOICE QUESTIONS)
  1. If the vectors ai +j + k , i-bj+k, i+j-ck are co-planar, then abc + 2 ...

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  2. If the vector ai+j+k,i+bj+k and i+j+ck are coplanar, then :

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  3. Let a,b,c be distinct non-negative numbers. If the vectors ahati+ahatj...

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  4. If veca , vecb , vec c are any three coplanar unit vectors , then :

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  5. If veca, vecb, vecc are three non-coplanar mutually perpendicular unit...

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  6. The vector vec(a) lies in the plane of vectors vec(b) and vec(c). Whi...

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  7. If a = i-j+k,b=i-2j-k and c=3i+pj+5k are coplanar, then p =

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  8. If l( b xx c) + m(c xxa) + n(a xx b) = 0 and at least one of l, m, n i...

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  9. The vectors (x,x+1,x+2),(x+3,x+3,x+5) and (x+6,x+7,x+8) are coplanar f...

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  10. If the vectors, a,b,c are coplanar, then

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  11. Let veca = 2i + j+k, vecb = i+ 2j -k and a unit vector vecc be coplana...

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  12. IF (sec^2A)hati+hatj+hatk, hati+(sec^2 B)hatj+hatk and hati+hatj+(sec^...

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  13. A unit vector coplanar with i+j+2k and i+2j+k and perpendicular to i+j...

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  14. The vector r = a xx(b xxc) is

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  15. Given, two vectors are hati - hatj and hati + 2hatj, the unit vector c...

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  16. The unit vector which is orthogonal to a =3i+2j+6k and coplanar with b...

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  17. If a = (-1,1,1) and b = (2,0,1) then the vector r satisfying the condi...

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  18. If a, b, c are three unit vectors such that a xx (b xx c) = (1)/(2)b ...

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  19. If vec a , vec ba n d vec c are non-coplanar unit vectors such tha...

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  20. If a is perpendicular to b and c, then

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