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If ` vec u , vec va n d vec w` are three non-cop0lanar vectors, then prove that `( vec u+ vec v- vec w)dot( vec u- vec v)xx( vec v- vec w)= vec udot vec vdotxx vec w`

A

0

B

`[uvw]`

C

`u .wxxv`

D

`3u.vxxw`

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

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

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

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

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

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

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  7. The resultant of two forces P N and 3 N is a force of 7 N. If the d...

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  8. a =hati+hatj-hatk,b= hati-2hatj+hatk,c=hati-hatj-hatk, then a vector i...

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  9. Let a =i-j,b=j-k,c=k-i. If d is a unit vector such that a.d =0 = [vecb...

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  10. x,y,z are distinct scalars such that [xa+yb+zc, xb+yc+za, xc+ya+zb] =0...

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  11. If l,j,k are the usual three perpendicular unit vectors then the val...

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  12. Write the value of hat idot( hat jxx hat k)+ hat jdot( hat kxx hat i)...

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  13. If a =i+j-k,b=i-j+k andc=i-j-k then axx(bxxc) =

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  14. If a,b,c be three non-coplanar vectors, then (i) [a-b,b-c,c-a]=

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

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

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

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

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

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

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