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Find the value of c for which the vecto...

Find the value of `c` for which the vectors ` vec a=(clog_2x) hat i-6 hat j+3 hat k` and `vec b=((log)_2x) hat i+2 hat j+(2c(log)_2x) hat k` make an obtuse angle for any `x in (0,oo)` .

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RD SHARMA-SCALAR OR DOT PRODUCT-Solved Examples And Exercises
  1. If vec a , vec b , vec c are unit vector, prove that | vec a- vec b|...

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  2. If vec a , vec b , vec c are mutually perpendicular unit vectors, fin...

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  3. Find the value of c for which the vectors vec a=(clog2x) hat i-6 hat...

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  4. Let vec a= hat i+4 hat j+2 hat k ,\ \ vec b=3 hat i-\ 2 hat j+7 hat ...

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  5. Dot products of a vector with vectors 3 hat i-5 hat k ,2 hat i+7 hat j...

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  6. Let vec a , vec b , vec c be three vectors such that | vec a|=1,| vec...

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  7. (Cosine Formulae) if a ,b ,c are the lengths of the sides opposite res...

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  8. Prove that the altitudes of a triangle are concurrent.

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  9. Find the components of a unit vector which is perpendicular to the v...

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  10. If a unit vector vec a makes angle pi//4 with hat i ,pi//3 with hat...

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  11. If hat aa n d hat b are unit vectors inclined at an angle theta , t...

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  12. If two vectors vec aa n d vec b are such that |veca|=2, |vecb|=3 and ...

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  13. Find | vec a|a n d| vec b|,if( vec a - vec b)dot ( vec a+ vec b) =27an...

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  14. If two vectors vec aa n d vec b are such that | vec a|=2,| vec b|=3a ...

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  15. Show that the projection vector vec aa n d vec b(!= vec0)(com pon e n...

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  16. Using dot product of vectors, prove that a parallelogram, whose dia...

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  17. For any three vectors vec a , vec b , vec c , prove that | vec a+ v...

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  18. Show that the angle between two diagonals of a cube is cos^(-1)(1/3)do...

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  19. Find ( vec a+3 vec b).(2 vec a- vec b), If vec a= hat i+ hat j+2 hat ...

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  20. Find the angle between two vectors vec a , vec b having the same le...

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