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Show that ( vec axx vec b)^2=| vec a|^2|...

Show that `( vec axx vec b)^2=| vec a|^2| vec b|^2-( vec adot vec b)^2=| [vec a.vec a, vec a.vec b],[ vec a.vec b, vec b.vec b]|`

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As we know, `vec axx vec b
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RD SHARMA-VECTOR OR CROSS PRODUCT -Solved Examples And Exercises
  1. Let vec a , vec b , vec c be unit vectors such that vec adot vec b= ...

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  2. Prove by vector method that sin(A-B)=sinAcosB-cosAsinB and sin(A+B)=si...

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  3. Show that ( vec axx vec b)^2=| vec a|^2| vec b|^2-( vec adot vec b)^2=...

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  4. Given | vec a|=10 ,| vec b|=2 "and" vecadot vec b=12 ,"find"| vec axx ...

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  5. If A(0,1,1),B(2,3,-2),C(22 ,19 ,-5)a n dD(1,-12 ,1) are the vertices o...

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  6. Find the area of the parallelogram determined by the vectors hat i+2 ...

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  7. Find a unit vector perpendicular to the plane A B C , where the coordi...

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  8. Find a vector of magnitude 9, which is perpendicular to both vectors 4...

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  9. Find a unit vector perpendicular to both the vectors hat i-2 hat j+3 ...

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  10. For any vector vec a , prove that | vec axx hat i|^2+| vec axx hat j|...

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  11. Find the magnitude of vec a give by vec a=( hat i+2 hat j-2 hat k)xx...

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  12. Find vec axx vec b ,\ if\ vec a=2 hat i+ hat k\ a n d\ vec b= hat i...

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  13. Find lambda and mu if (2 hat i+6 hat j+27 hat k)xx( hat i+lambda hat j...

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  14. If vec r=x hat i+y hat j+z hat i ,\ find the value of ( vec rxx hat ...

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  15. Find a unit vector perpendicular to each of the vectors ( -> a+ -> ...

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  16. Let vec a= hat i- hat j ,\ vec b=3 hat j- hat k\ a n d\ vec c=7 hat...

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  17. Show that the area of a parallelogram having diagonals 3 hat i+ hat j-...

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  18. Find the area of the triangle whose vertices are A(3,-1,2),\ B(1,-1,-3...

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  19. If vec axx vec b= vec cxx vec d\ a n d\ vec axx vec c= vec bxx vec d...

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  20. Prove that ( vec a- vec b)xx( vec a+ vec b)=2( vec axx vec b) and inte...

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