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Let vec a= vec i- vec k , vec b=x vec i...

Let ` vec a= vec i- vec k , vec b=x vec i+ vec j+(1-x) vec k` and ` vec c=y vec i+x vec j+(1+x-y) vec k` . Then `[ vec a vec b vec c]` depends on only `x` (b) only `y` Neither `xnory` (d) both `xa n dy`

A

only x

B

only y

C

neither x nor y

D

both x and y

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The correct Answer is:
C
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ML KHANNA-ADDITION AND MULTIPLICATION OF VECTORS -Problem Set (3) (MULTIPLE CHOICE QUESTIONS)
  1. The edges of a parallelopiped are of unit length and a parallel to non...

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  2. The volume of the tetrahedron whose vertices are points A(1,-1,10), B ...

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  3. Let vec a= vec i- vec k , vec b=x vec i+ vec j+(1-x) vec k and vec c...

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  4. The value of a so that the volume of parallelopiped formed by vectors ...

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  5. Let vecb=-veci+4vecj+6veck, vecc=2veci-7vecj-10veck. If veca be a unit...

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  6. Let a =3i+2k and b=2j+k. If c is a unit vector, then the maximum value...

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  7. Let veca,vecb and vecc be three vectors. Then scalar triple product [v...

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  8. For three vectors vecu,vecv,vecw which of the following expressions is...

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  9. If veca, vecb, vecc are non-coplanar vectors, then (veca.(vecbxxvecc))...

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  10. If vecd = gamma(veca xx vecb) + mu(vecb xx vecc) + v(vecc xx veca) and...

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  11. If a, b, c are non-coplanar vectors and r is a unit vector, then |(r....

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  12. Let veca=a(1)hati+a(2)hatj+a(3)hatk,vecb=b(2)hatj+b(3)hatk and vecc=c(...

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  13. The scalar vec Adot( vec B+ vec C)xx( vec A+ vec B+ vec C) equals 0 b...

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  14. If [(3a + 5b) (c) (d)] = p [acd] + q[bcd], them p + q=

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  15. (a + 2b-c).[(a-b) xx (a-b-c)] is equal to

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  16. If a, b and c three non-coplanar vectors, then (a + b +c). [a+b) xx (a...

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  17. If vec u , vec va n d vec w are three non-cop0lanar vectors, then ...

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  18. If vec a , vec ba n d vec c are unit coplanar vectors, then the sc...

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  19. If a,b,c ar enon-coplanar vectors and lamda is a real number, then the...

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  20. If bara,barb,barc are non-coplanar vectors and lambda is a real number...

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