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(Apollonius theorem): If D is the midpoi...

(Apollonius theorem): If D is the midpoint of the side BC of a triangle ABC, then show by vector method that
` |vec(AB)|^(2) + |vec(AC)|^(2) = 2(|vec(AD)|^(2)+ |vec(BD)|^(2)). `

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PREMIERS PUBLISHERS-APPLICATIONS OF VECTOR ALGEBRA-PROBLEMS FOR PRACTICE (Answer the following questions)
  1. (Apollonius theorem): If D is the midpoint of the side BC of a triangl...

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  2. Prove that the sum of the squares of the squares of tha diagonals of a...

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  3. Show that (veca xx vecb) *(vecc xx vecd) +(vecb xx vecc) *(veca xx vec...

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  4. Find the vector and cartesian equation of the line through the point (...

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  5. Find the vector and cartesian equation of the line joining the points ...

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  6. Find the angle between the lines (x-1)/(2)=(y+1)/(3)=(z-4)/(6) and vec...

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  7. Find the distance between the parallel lines vecr=(hati-hatj)+t(2hati-...

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  8. Show that the lines vecr=(hati-hatj)+t(2hati+hatk) and vecr=(2hati-hat...

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  9. Find the vector and cartesian equation of a plane which is at a distan...

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  10. Find the vector and cartesian equation of the plane passing through (2...

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  11. Find the vector and cartesian equation of the plane passing through (2...

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  12. Find the Vector and Cartesian equation of the plane containing the lin...

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  13. Find the vector cartesian equation of the plane passing through the po...

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  14. Find the vector and certesian equation of the plane through the points...

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  15. Find the equation of the plane passing through the points (3, 4, 2), (...

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  16. Find the equation of the plane passingthrough the intersection of the...

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  17. Find the distance between the parallel planes vecr*(-hati-hatj+hatk)=3...

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  18. Find the coordinates of the point where the line vecr=(hati+2hatj-5ha...

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  19. The value of [hati+hatj,hatj+hatk,hatk+hati] is equal to :

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  20. If abs(veca+vecb)=abs(veca-vecb) prove that veca and vecb are perpendi...

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  21. Find the shortest distance between the lines (x-3)/(3)=(y-8)/(-1)=(z-3...

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