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Prove that the altitudes of a triangle a...

Prove that the altitudes of a triangle are concurrent.

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RD SHARMA ENGLISH-SCALAR OR DOT PRODUCT-All Questions
  1. Let vec a , vec b , vec c be three vectors such that | vec a|=1,| vec...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. 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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