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If l( b xx c) + m(c xxa) + n(a xx b) = 0...

If `l( b xx c) + m(c xxa) + n(a xx b) = 0` and at least one of l, m, n is not zero then the vectors, a, b and c are

A

parallel

B

coplanar

C

mutually perpendicular

D

none

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The correct Answer is:
B
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ML KHANNA-ADDITION AND MULTIPLICATION OF VECTORS -Problem Set (3) (MULTIPLE CHOICE QUESTIONS)
  1. The vector vec(a) lies in the plane of vectors vec(b) and vec(c). Whi...

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

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  3. 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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  4. 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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  5. If the vectors, a,b,c are coplanar, then

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

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

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

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

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

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

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

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

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

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

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  16. If a vector veca is expressed as the sum of two vectors vec(alpha) and...

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  17. u = a xx (b xx c) + b xx ( c xx a) + c xx ( a xx b) , then

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

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  19. If a = i+j+k and b=i-j then the vectors (a.i)i+(a.j)j+(a.k)k, (b...

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  20. [abi]i+[abj]j+[abk]k is a equal to

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