Find the value of t for which the points (1,-1),(3,-3) and (t,2) lie on the same line (using determinants).

Find the set of positive values of b for which the origin and the point (1,1) lie on the same side of the straight line,a^(2)x+aby+1=0,AA a in R

By using determinants , find the value of 'y' for which the points (1,3),(2,5) and (3,y) are collinear.

Find the range of values of t for which 2sin t=(1-2x+5x^(2))/(3x^(2)-2x-1)

If 5a+5b+20c=t, then find the value of t for which the line ax+by+c-1=0 always passes through a fixed point.

Find the locus of the point (t^(2)-t+1,t^(2)+t+1),t in R

Find the coordinates of the point where the line through (3,4,5) and (2,3,1) crosses the plane determined by points A(1,2,3),B(2,2, 1) and C(-1,3

If 5a+5b+20c=t then find the values of t for which the line ax+by+c-1=0 always passes through a fixed point

find the range of values of t for which 2sin t=(1-2x+5x^(2))/(3x^(2)-2x-1)

If t is a real number satisfying the equation 2t^(3)-9t^(2)+30-a=0, then find the values of the parameter a for which the equation x+(1)/(x)=t gives six real and distinct values of x .

Prove that the points A(1, 4), B(3, -2) and C(4, -5) are collinear. Also find the equation of the line on which these points lie.