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If vec axx vec b= vec axx vec c , vec a...

If ` vec axx vec b= vec axx vec c , vec a!= vec0a n d vec b!= vec c` , show that ` vec b= vec c+t vec a` for some scalar `tdot`

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`vecbxxveca=vecaxxvecc`

`vecbxxveca-vecaxxvecc=0`

`vecbxxveca-veccxxveca=0`

`(vecb−vecc)xxveca=0`

this means vectors (b-c) and b are parallel so they lie in same plane ...
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RD SHARMA-VECTOR OR CROSS PRODUCT -Solved Examples And Exercises
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  2. Prove that the normal to the plane containing three points whose po...

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  3. If vec axx vec b= vec axx vec c , vec a!= vec0a n d vec b!= vec c , s...

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  4. If veca , vec b , vec c are the position vectors of the vertices A ,B ...

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  5. For any three vectors veca , vec b , vec c show that vecaxx( vec b+ ...

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  7. Prove that the points A ,Ba n d C with position vectors vec a , vec b...

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  8. Let vec a , vec b , vec c are three non-zero vectors such that vec a...

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  9. If vec a ,\ vec b ,\ vec c are three vectors such that vec adot...

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  10. If vec a , vec b , vec c are three vectors such that | vec a+ vec b+ ...

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  11. Let vec a=2 hat i+ hat k , vec b= hat i+ hat j+ hat ka n d vec c=4 ha...

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  12. If vec a , vec ba n d vec c are three non coplanar vectors, then p...

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  13. Let vec a , vec b , vec c be unit vectors such that vec adot vec b= ...

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

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

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

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

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

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