If `x_1,x_2,x_3` as well as `y_1, y_2, y_3` are in G.P. with same common ratio, then prove that the points `(x_1, y_1),(x_2,y_2),a n d(x_3, y_3)` are collinear.

If x_1,x_2,x_3 as well as y_1,y_2,y_3 are in G P with the same common ratio, then the points (x_1,y_1),(x_2,y_2), and (x_3, y_3)dot (a)lie on a straight line (b)lie on an ellipse (c)lie on a circle (d) are the vertices of a triangle.

If x_(1),x_(2),x(3) as well as y_(1),y_(2),y_(3) are in geometric progression with the same common ratio,then the points (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3))

If x_(1), x_(2), x_(3) and y_(1),y_(2), y_(3) are in arithmetic progression with the same common difference then the points (x_(1),y_(1)) (x_(2),y_(2)) (x_(3), y_(3)) are:

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 normals to the ellipse x^2/a^2+y^2/b^2= 1 at the points (X_1, y_1), (x_2, y_2) and (x_3, y_3) are concurrent, prove that |(x_1,y_1,x_1y_1),(x_2,y_2,x_2y_2),(x_3,y_3,x_3y_3)|=0 .

If three point A(x_(1), y_(1)), B(x_(2), y_(2)) and C(x_(3), y_(3)) will be collinear then the area of triangleABC= ____.

Statement 1:If the point (2a-5,a^2) is on the same side of the line x+y-3=0 as that of the origin, then a in (2,4) Statement 2: The points (x_1, y_1)a n d(x_2, y_2) lie on the same or opposite sides of the line a x+b y+c=0, as a x_1+b y_1+c and a x_2+b y_2+c have the same or opposite signs.

The value of |(1,1,1),(2x,2y,2z),(3x,3y,3z)| is ____