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Find | vec a|a n d| vec b|,if( vec a - v...

Find `| vec a|a n d| vec b|,if( vec a - vec b)dot ( vec a+ vec b) =27`and`| vec a|=2| vec b|dot`

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RD SHARMA ENGLISH-SCALAR OR DOT PRODUCT-All Questions
  1. If hat aa n d hat b are unit vectors inclined at an angle theta , t...

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

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

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  4. If two vectors vec a and vec b are such that | vec a|=2,| vec b|=1...

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  5. For any two vectors vec a and vec b , prove that: | vec a+ vec b|...

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

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

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

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

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

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  11. Find the angle between two vectors vec a\ a n d\ vec b having the...

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  12. If hat i+ hat j+ hat k ,\ 2 hat i+5 hat j ,\ 3 hat i+2 hat j-3 hat k\...

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  13. Let vec a\ a n d\ vec b be two vectors of the same magnitude such th...

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  14. Find | vec x| if for a unit vector vec a ,\ ( vec x- vec a)dot \ ( ve...

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  15. If vec a=5 hat i- hat j-3 hat k ,\ a n d\ vec b= hat i+3 hat j-5 hat...

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  16. If vec a+ vec b+ vec c= vec0,\ vec|a|=3,\ | vec b|=5\ a n d\ | vec c...

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  17. For any vector vec a\ a n d\ vec b prove that | vec a+ vec b|lt=| ve...

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  18. For any two vectors vec a and vec b prove that ( veca dot vecb)^2le|...

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  19. If vec a ,\ vec b ,\ are two vectors such that | vec a+ vec b|=| ve...

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  20. The scalar product of the vector vec a= hat i+ hat j+ hat k with a un...

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