Prove that the straight lines `x/alpha=y/beta=z/gamma,x/l=y/m=z/n and x/(a alpha)=y/(b beta)=z/(c gamma)` will be co planar if `l/alpha(b-c)+m/beta(c-a)+n/gamma(a-b)=0`

Show that the lines (x-a+d)/(alpha-delta)=(y-a)/(alpha)=(z-a-d)/(alpha+delta)(x-b+c)/(beta-gamma)=(y-b)/(beta)=(z-b-c)/(beta+gamma) are coplanar.

The equations of the line through the point (alph, beta, gamma) and equally inclined to the axes are (A) x-alphay-beta=z-gamma (B) (x-1)/alpha=(y-1)/beta=(z-1)/gamma (C) x/alpha=y/beta=z/gamma (D) none of these

If 0

If alpha,beta,gamma are the cube roots of p, then for any x,y,z(x alpha+y beta+z gamma)/(x beta+y gamma+z alpha)=

If alpha,beta,gamma are different from 1 and are the roots of ax^(3)+bx^(2)+cx+d=0 and (beta-gamma)(gamma-alpha)(alpha-beta)=(25)/(2) ,then prove that det[[(alpha)/(1-alpha),(beta)/(1-beta),(gamma)/(1-gamma)(alpha)/(1-alpha),(beta)/(1-beta),(gamma)/(1-gamma)alpha,beta,gammaalpha^(2),beta^(2),gamma^(2)]]=(25d)/(2(a+b+c+d))

If alpha,beta,gamma are the cube roots of p then for any x,y and z(x alpha+y beta+z gamma)/(x beta+y gamma+z alpha) is