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) and (x-b+c)/(beta-gamma)=(y-b)/beta=(z-b-c)/(beta+gamma) are coplanar.

The equations of the line through the point (alpha, beta, gamma) and equally inclined to the axes are (A) x-alpha=y-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 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 =

cos alpha sin (beta-gamma) + cos beta sin (gamma-alpha) + cos gamma sin (alpha-beta)=

If alpha , beta , gamma are the roots of x^3 + qx +r=0 then (1)/( alpha + beta - gamma) +(1)/( beta + gamma - alpha) +(1)/(gamma + alpha - beta) =

If alpha , beta , gamma are the roots of x^3 + qx +r=0 then (1)/( alpha + beta - gamma) +(1)/( beta + gamma - alpha) +(1)/(gamma + alpha - beta) =

If the straight line (x-alpha)/(l)=(y-beta)/(m)=(z-gamma)/(n) intersect the curve ax^2+by^2=1, z=0, then prove that a(alphan-gammal)^2+b(betan-gammam)^2=n^2

If alpha , beta , gamma are roots of the equation x^3 + ax^2 + bx +c=0 then alpha^(-1) + beta^(-1) + gamma^(-1) =

Determine the values of alpha ,beta , gamma when [{:( 0, 2beta, gamma),( alpha ,beta, -gamma),( alpha ,-beta, gamma):}] is orthogonal.

If alpha, beta. gamma are the roots of x^3 + px^2 + q = 0, where q=0, ther Delta=[(1/alpha,1/beta,1/gamma),(1/beta,1/gamma,1/alpha),(1/gamma,1/alpha,1/beta)] equals (A) alpha beta gamma (B) alpha +beta + gamma (C) 0 (D) none of these