[" 21.If the join of "(x,y_(1))" and "(x_(2),y_(2))" makes an obtuse "],[" angle at "(x_(3),y_(3))," then prove that "(x_(3)-x_(1))(x_(3)-x_(2))],[+(y_(3)-y_(1))(y_(3)-y_(2))<0]

If the join of (x_(1),y_(1)) and (x_(2),y_(2)) makes on obtuse angle at (x_(3),y_(3)), then prove than (x_(3)-x_(1))(x_(3)-x_(2))+(y_(3)-y_(1))(y_(3)-y_(2))<0

If the join of (x_1,y_1) and (x_2,y_2) makes on obtuse angle at (x_3,y_3), then prove that (x_3-x_1)(x_3-x_2)+(y_3-y_1)(y_3-y_2)<0

If the join of (x_1,y_1) and (x_2,y_2) makes on obtuse angle at (x_3,y_3), then prove that (x_3-x_1)(x_3-x_2)+(y_3-y_1)(y_3-y_2)<0

If the join of (x_1,y_1) and (x_2,y_2) makes on obtuse angle at (x_3,y_3), then prove than (x_3-x_1)(x_3-x_2)+(y_3-y_1)(y_3-y_2)<0

If the points (x_(1),y_(1)),(x_(2),y_(2)), and (x_(3),y_(3)) are collinear show that (y_(2)-y_(3))/(x_(2)x_(3))+(y_(3)-y_(1))/(x_(3)x_(1))+(y_(1)-y_(2))/(x_(1)x_(2))=0

If three points (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)) lie on the same line,prove that (y_(1)-y_(3))/(x_(2)x_(3))+(y_(3)-y_(1))/(x_(3)x_(1))+(y_(1)-y_(2))/(x_(1)x_(2))=0

If the tangent at (x_(1),y_(1)) to the curve x^(3)+y^(3)=a^(3) meets the curve again in (x_(2),y_(2)), then prove that (x_(2))/(x_(1))+(y2)/(y_(1))=-1

An equilateral triangle has each side to a. If the coordinates of its vertices are (x_(1), y_(1)), (x_(2), y_(2)) and (x_(3), y_(3)) then the square of the determinat |(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1)|^2 equals

An equilateral triangle has each side equal to a. If the coordinates of its vertices are (x_(1), y_(1)), (x_(2), y_(2)) and (x_(3), y_(3)) then the square of the determinant |(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1)| equals

An equilateral triangle has each side to a. If the coordinates of its vertices are (x_(1), y_(1)), (x_(2), y_(2)) and (x_(3), y_(3)) then the square of the determinat |(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1)| equals