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Find the values of ' a ' which the vecto...

Find the values of `' a '` which the vector ` vec r=(a^2-4) hat i+2 hat j-(a^2-9) hat k` makes acute angle with the coordinate axes.

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RD SHARMA ENGLISH-SCALAR OR DOT PRODUCT-All Questions
  1. Find the value of lambda so that the vectors vec a=2 hat i+lambda hat...

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  2. Find the value of p for which the vectors vec a=3 hat i+2 hat j+9 ha...

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  3. Find the values of ' a ' which the vector vec r=(a^2-4) hat i+2 hat j...

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  4. If vec a , vec b , vec c are unit vector, prove that | vec a- vec b|...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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