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Using vectors: Prove that if a,b,care th...

Using vectors: Prove that if a,b,care the lengths of three sides of a triangle then its area `Delta` is given by `Delta= sqrt(s(s-a)(s-b)(s-c))` where 2s=a+b+c

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RD SHARMA ENGLISH-VECTOR OR CROSS PRODUCT -All Questions
  1. If vec a=3 hat i- hat j-2 hat k and vec b=2 hat i+3 hat j+ hat k , ...

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  2. If vec a=3 hat i-2 hat k and vec b=- hat i+3 hat k , find | veca x...

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  3. Using vectors: Prove that if a,b,care the lengths of three sides of a ...

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  4. Prove by vector method that the parallelogram on the same base and ...

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  5. If D ,E ,F are the mid-points of the sides B C ,C Aa n dA B respective...

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  6. Let vec O A= vec a , vec O B=10 vec a+2 vec b ,a n d vec O C=bw h e r...

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  7. A B C D is quadrilateral such that vec A B= vec b , vec A D= vec d , ...

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  8. If veca , vec b , vec c are three vectors such that veca+ vec b+ vec...

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  9. Prove that the normal to the plane containing three points whose po...

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  10. If vec axx vec b= vec axx vec c , vec a!= vec0a n d vec b!= vec c , s...

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  11. For any two vectors vec aa n d vec b , show that (1+| vec a|^2)(1+| v...

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  12. If veca , vec b , vec c are the position vectors of the vertices A ,B ...

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  13. For any three vectors veca , vec b , vec c show that vecaxx( vec b+ ...

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  14. Show that perpendicular distance of the point vec c from the line joi...

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  15. Prove that the points A ,Ba n d C with position vectors vec a , vec b...

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  16. Let vec a , vec b , vec c are three non-zero vectors such that vec a...

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  17. If vec a ,\ vec b ,\ vec c are three vectors such that vec adot\...

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  18. If vec a , vec b , vec c are three vectors such that | vec a+ vec b+ ...

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  19. Let vec a=2 hat i+ hat k , vec b= hat i+ hat j+ hat ka n d vec c=4 ha...

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  20. A triangle O A B is determined by the vectors vec aa n d vec b as sho...

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