If `A(cosalpha,sinalpha),B(sinalpha,-cosalpha),C(1,2)` are the vertices of ` A B C ,` then as `alpha` varies, find the locus of its centroid.

lim_(alphato pi/4)(sinalpha-cosalpha)/(alpha-pi/4) is

If A(-2, -1), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogram, find the values of a and b.

If F (alpha)= [{:(cosalpha,0, sinalpha),(0,1,0),(-sinalpha,0,cosalpha):}] Show that = F (alpha)^(-1)= F(-alpha)

Consider the matrix A_(alpha)=[(cosalpha,-sinalpha),(sinalpha,cosalpha)] Find all possible real values of alpha satisfying the condition A_(alpha)+A_(alpha)" "^(T)=I.

P(cosalpha,sinalpha), Q(cosbeta, sinbeta) , R(cosgamma, singamma) are vertices of triangle whose orthocenter is (0, 0) then the value of cos(alpha-beta) + cos(beta-gamma) + cos(gamma-alpha) is

Find the amplitude of sinalpha+i(1-cosalpha)

Consider the matrix A_(alpha)=[(cosalpha,-sinalpha),(sinalpha,cosalpha)] Show that A_(alpha)A_(beta)=A_(alpha+beta)

A(-3, 0), B(10, -2) and C(12, 3) are the vertices of triangleABC . Find the equation of the altitude through A and B.

If the points P(6,2) and Q(-2,1) and R are the vertices of a DeltaPQR and R is the point on the locus of y=x^(2)-3x+4 , then find the equation of the locus of centroid of DeltaPQR .