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If A D is the median of A B C , usin...

If `A D` is the median of ` A B C ,` using vectors, prove that `A B^2+A C^2=2(A D^2+C D^2)dot`

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RD SHARMA ENGLISH-SCALAR OR DOT PRODUCT-All Questions
  1. If the median to the base of a triangle is perpendicular to the bas...

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  2. If A D is the median of A B C , using vectors, prove that A B^2...

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  3. In a triangle O A B ,/A O B=90^0dot If P and Q are points of trisectio...

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  4. If hat a and hat b are unit vectors inclined at an angle theta , the...

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  5. (Pythagoras's Theorem) Prove by vector method that in a right angled...

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  6. Prove that; If the diagonals of a quadrilateral bisect each other a...

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  7. prove using vectors: The quadrilateral obtained by joining mid-poin...

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  8. prove by vector method that the sum of the squares of the diagonals...

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  9. prove that the diagonals of a rectangle are perpendicular if and on...

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  10. Using analytical geometry, prove that the diagonals of a rhombus are ...

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  11. If | vec a|=a and | vec b|=b , prove that ( vec a/(a^2)- vec b/(b^2))^...

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  12. If vec a= hat i- hat j and vec b=- hat j+2 hat k , find ( vec a-2 ve...

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  13. Find the angles which the vector vec a= hat i- hat j+sqrt(2) hat k ma...

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  14. Dot product of a vector with hat i+ hat j-3 hat k , hat i+3 hat j-2 h...

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  15. Find vec adot vec b , when (i) vec a= hat i-2 hat j+ hat k and ve...

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  16. For what value of lambda are the vector vec a and vec b perpendi...

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  17. If vec a and vec b are two vectors such that | vec a|=4,| vec b|=3 a...

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  18. Find the angles of a triangle whose vertices are A(0,-1,-2),B(3,1,4...

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  19. Find the projection of vec b+ vec c on vec a , where vec a = 2 hat ...

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  20. Find the values of x and y if the vectors vec a=3 hat i+x hat j...

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