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If O be the origin and if coordinates o...

If O be the origin and if coordinates of any two points `Q_(1) and Q_(2)` be `(x_(1),y_(1)) and (x_(2),y_(2))` respectively, prove that `overline(OQ_(1))* overline(OQ_(2)) cos angle Q_(1)OQ_(2)=x_(1)x_(2)+y_(1)+y_(2)`.

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CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-COORDINATE GEOMETRY (TWO DIMENSIONAL COORDINATE GEOMETRY)
  1. If O be the origin and if coordinates of any two points Q(1) and Q(2)...

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  2. The ends of a rod of length l move on two mutually perpendicular lines...

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  3. If the coordinates of the vertices A,B and C of Delta ABC be (x(1),y(1...

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  4. Prove that if P(x,y) be any point on the line segment joining P(1)(x...

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  5. Prove that if P(x,y) be any point on the line segment joining P(1)(x...

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  6. Prove that if P(x,y) be any point on the line segment joining P(1)(x...

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  7. Prove that if P(x,y) be any point on the line segment joining P(1)(x...

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  8. Prove that if P(x,y) be any point on the line segment joining P(1)(x...

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  9. (3,2) and (-3,2) are the vertices of an equilateral triangle which con...

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  10. Show that the points A(a,b), B(a+alpha+ b,+ beta), C(a+alpha+ p, b+bet...

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  11. Prove that it is impossible to have an equilateral triangle for which ...

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  12. A straight line moves in such a way that the algebraic sum of the perp...

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  13. The coordinates of two point opposite vertices oc a square are (3,4) a...

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  14. If L,M,N divide the sides BC,CA and AB of a triangle ABC in the same r...

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  15. Find the equation to the locus represented by x=(2+t+1)/(3t-2), y=(t-1...

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  16. Find the equation to the locus represented by the parametric equation...

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  17. If t is a variable parameter, then the equation to the locus defined b...

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  18. The four point A(a,0), B(b,0) ,C(c,0) and D(d,0) are such that a and b...

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  19. The straight lines y=x=2 and y=6x+3 are parallel to two sides of the r...

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  20. The eqution of the side BC,CA and AB of the triangle ABC are u(1)=a(1)...

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