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If origin is the orthocentre of a triang...

If origin is the orthocentre of a triangle formed bythe points `(cos alpha, sin alpha,0), (cos beta, sin beta,0), (cos gamma, sin gamma,0) ` then `sumcos(2alpha-beta-gamma)= ` -

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AAKASH SERIES-3D-COORDINATE SYSTEM-ADDITIONAL EXERCISE
  1. Find the area of the triangle whose vertices are (1,1,1),(1,2,3),(2,0,...

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  2. The transformed equation of 2x^2+3y^2-z^2-8x+18y+2z+9=0 when the axes ...

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  3. The point to which the axes should be translated to eliminate first de...

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  4. Find the ratio in which the centroid of tetrahedron ABCD divides the l...

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  5. The circumcentre of the triangle formed by the pointgs (1,2,3), (3,-1,...

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  6. The centroid of the triangle formed by the points (1,2,3),(2,3,1),(3,1...

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  7. Find the orthocenter of the triangle formed by the points (2,1,5),(3,2...

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  8. Find the orthocenter of the triangle formed by the points (2,-1,1),(1,...

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  9. If ("Cos"alpha, "Sin"alpha,0),(cos beta, sin beta,0), (cos gamma, sin ...

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  10. If origin is the orthocentre of a triangle formed bythe points (cos al...

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  11. If the orthocentre and the centroid of a triangle are (-3,51),(3,3,-1)...

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  12. If the orthocentre and the circucentre of are (-3,5,2) ,(6,2,5) then i...

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  13. If (2, 5, 1) and (9, 10, 5) are the ends of a diagonal of a rectangul...

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  14. If L and M are the feet of the perpendiculars from the point (2,4,5) t...

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  15. If A,B are the feet of the perpendicular from P (2,4,5) to the x-axis ...

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  16. The locus of a point P from which the distance to the point (1,1,1) is...

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  17. Find the equation to the locus of the point for which the sum of the s...

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  18. The locus of the point P such that PA + PB = 4 where A=(2,3,4) , B=(-2...

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  19. Prove that the line segment joining the midpoints of the two sides of ...

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  20. Find the ratios in which the join of (12,-4,8) and (27,-9,18) is inter...

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