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If D ,E ,F are the mid-points of the sid...

If `D ,E ,F` are the mid-points of the sides `B C ,C Aa n dA B` respectively of a triangle `A B C ,` prove by vector method that `A r e aof D E F=1/4(a r e aof A B C)dot`

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RD SHARMA ENGLISH-VECTOR OR CROSS PRODUCT -All Questions
  1. Using vectors: Prove that if a,b,care the lengths of three sides of a ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  19. If A ,B ,C ,D be any four points in space, prove that | vec A Bxx vec ...

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  20. If vec a , vec ba n d vec c are three non coplanar vectors, then pr...

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