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The Cartesian equation of the sides BC,C...

The Cartesian equation of the sides BC,CA, AB of a triangle are respectively `u_(1)=a_(1)x+b_(1)y+c_(1)=0, u_(2)=a_(2)x+b_(2)y+c_(2)=0` and `u_(3)=a_(3)x+b_(3)y+c_(3)=0`. Show that the equation of the straight line through A bisectig the side `bar(BC)` is `(u_(3))/(a_(3)b_(1)-a_(1)b_(3))=(u_(2))/(a_(1)b_(2)-a_(2)b_(1))`

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`(u_(2))/(a_(1)b_(2)-a_(2)b_(1))`
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AAKASH SERIES-STRAIGHT LINES-SOLVED EXAMPLES
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  2. Find the incentre of the triangle formed by x+y-7=0,x-y+1=0,x-3y+5=0.

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  3. A triangle is formed by the lines ax+by+c=0, lx+my+n=0 and px+qy+r=0. ...

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  4. The Cartesian equation of the sides BC,CA, AB of a triangle are respec...

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  5. Find the acute angle between the lines y+2=0 and sqrt(3)x+y-1=0.

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  6. Find the value of k if the lines 2x+ky-10=0 and 5x+2y-7=0 are parallel...

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  7. Find the value of k if the lines (3x+4y+5)-k(x+y+3)=0 is (i) paral...

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  8. The lines 3x-ky-2=0 and 2x+y+2=0 are perpendicular find k.

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  9. The angle between the lines 3x-y-1=0 and 2x+ky+5=0 is 45^(@) find k

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  10. Find the angles of the triangle whose sides are x+y-4=0, 2x+y-6=0, 5x+...

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  11. If the four straight lines ax+by+p=0, ax+by+q=0, cx+dy+r=0 and cx+dy+s...

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  12. Find the foot of the perpendicular drawn from (-1,3) on the line 5x-y-...

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  13. Show that the feet of the perpendicular from (-2,-8) to the lines x-2y...

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  14. Find the image of (1-2) in the line 2x-3y+5=0.

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  15. x+y=4 is the perpendicular bisector of bar(AB) where A=(3,-3) Find B.

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  16. Find the product [{:(0,c,-b),(-c,0,a),(n,-a,0):}][{:(a^2,ab,ac),(ab,b^...

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  17. The hypotenuse of a right angled isosceles triangle has its ends at th...

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  18. A line is such that its segment between the lines 5x-y+4=0 and 3x+4y-4...

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  19. An equilateral triangle has its incentre at the origin and one side as...

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  20. A ray of light coming from the point (1,2) is reflected at a point A o...

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