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In a quadrilateral A B C D , prove that ...

In a quadrilateral `A B C D ,` prove that `A B^2+B C^2+C D^2+D A^2=A C^2+B D^2+4P Q^2,` where `P` and `Q` are middle points of diagonals `A C` and `B Ddot`

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RD SHARMA ENGLISH-SCALAR OR DOT PRODUCT-All Questions
  1. In A B C , A D is a median. Prove that A B^2+A C^2=2\ A D^2+2\ D C...

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  2. If the median to the base of a triangle is perpendicular to the bas...

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  3. In a quadrilateral A B C D , prove that A B^2+B C^2+C D^2+D A^2=A C^2+...

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  4. What is the angle between vectors vec a\ a n d\ vec b with magnitude...

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  5. If vec a\ a n d\ vec b are two vectors such that vec adot vec b=6,\...

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  6. Find the cosine of the angle between the vectors 4 hat i-3 hat j+3 hat...

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  7. If the vectors 3 hat i+m hat j+ hat k\ a n d\ 2 hat i- hat j-8 hat k a...

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  8. If the vectors 3 hat i-2 hat j-4 hat k\ a n d\ 18 hat i-12 hat j-m hat...

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  9. If vec a\ a n d\ vec b are vectors of equal magnitude, write the val...

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  10. If vec a\ a n d\ vec b are two vectors such that ( vec a+ vec b)dot(...

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  11. For any two vectors vec a\ a n d\ vec b write when | vec a+ vec b|=|...

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  12. For any two vectors vec a\ a n d\ vec b write then | vec a+ vec b|=|...

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  13. If vec a\ a n d\ vec b are two vectors of the same magnitude incline...

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  14. If vec adot vec adot=0\ a n d\ vec adot vec b=0 what can you conclud...

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  15. If vec b is a unit vector such that ( vec a+ vec b)dot ( (vec a- vec ...

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  16. If hat a ,\ hat b are unit vector such that\ hat a+ hat b is a unit...

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  17. If | vec a|=13 ,\ | vec b|=5\ a n d\ vec adot vec b=60 , t h e n find...

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  18. If vec a= hat i- hat j\ a n d\ vec b=- hat j+ hat k find the project...

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  19. For any two non zero vectors write the value of (| vec a+ vec b|^2+| v...

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  20. Write the the projections of vec r=3 hat i-4 hat j+12 hat k on the co...

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