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.

Prove that |(2,alpha+beta+gamma+delta,alphabeta+gammadelta),(alpha+beta+gamma+delta,2(alpha+beta)(gamma+delta),alpha beta(gamma+delta)+gamma delta(gamma+beta)),(alpha beta+gamma delta,alpha beta(gamma+delta)+gammadelta(alpha+beta),2alphabeta gamma delta)| = 0

If alpha , beta , lambda are three real numbers and A=[(1,cos(alpha-beta),cos(alpha-gamma)),(cos(beta-alpha),1,cos(beta-gamma)),(cos(gamma-alpha),cos(gamma-beta),1)] , then which of following is not true A)A is singular B)A is symmetric C)A is orthogonal D)A is not invertible

If a, b and c are in geometric progression and the roots of the equations ax^(2)+2bx+c=0 are alpha and beta and those cx^(2)+2bx+a=0 are gamma and delta , then : a) alpha ne beta ne gamma ne delta b) alpha ne beta and gamma ne delta c) alpha=abeta=cgamma=cdelta d) alpha=beta and gamma ne delta

If alpha,beta,gamma are roots of the equation x^(2) (px+q)=r(x+1), then the value of determinant |(1+alpha,1,1),(1,1+beta,1),(1,1,1+gamma)| is a) alpha beta gamma b) 1+(1)/(alpha)+(1)/(beta)+(1)/(gamma) c)0 d)None of these

If cot alpha cot beta=2 , show that (cos (alpha+beta))/(cos (alpha-beta))=(1)/(3)

If f(x) = a + bx + cx^(2) and alpha, beta, gamma are roots of the equation x^(3) = 1 , then |(a,b,c),(b,c,a),(c,a,b)| is equal to a) f(alpha) + f(beta) + f(gamma) b) f(alpha)f(beta) + f(beta)f(gamma) + f(gamma)f(alpha) c) f(alpha)f(beta)f(gamma) d) -f(alpha)f(beta)f(gamma)

Let A=[(0,2beta,gamma),(alpha,beta,-gamma),(alpha,-beta,gamma)] be 3xx3 matrix Find A^T

If alpha, beta are the roots of x^(2)-a(x-1)+b=0 , then find the value of (1)/(alpha^(2)-a alpha)+(1)/(beta^(2)-a beta)+(2)/(a+b)