If `alpha, beta, gamma` are the angle made by a vector with the coordinate axes, then `sin^(2) alpha + sin^(2) beta + sin^(2) gamma =`

If alpha+beta+gamma=2 pi, then

If cos alpha, cos beta, cos gamma are the direction cosines fo a vector veca, then cos 2alpha + cos 2beta + cos 2gamma is equal to

If cos alpha + 2 cos beta + 3 cos gamma = 0 , sin alpha + 2 sin beta + 3 sin gamma = 0 and alpha + beta + gamma = pi , then sin 3 alpha + 8 sin 3 beta + 27 sin 3 gamma =

If 1, omega, omega^(2) are the three cube roots of unity and alpha, beta, gamma are the cube roots of p, plt0 , then for any x, y, z the expression (x alpha+y beta+z gamma)/(x beta+y gamma+z alpha)=

If a line makes angle alpha,beta,gamma with the axes respectively, then cos 2alpha+cos 2beta + cos 2gamma =

A line makes acute alpha, beta and gamma with the coordinate axes such that cos alpha . Cos beta = cos beta . Cos gamma = 2/9 and cos gamma . cos alpha = 4/9 , then cos alpha + cos beta + cos gamma =

Let alpha, beta, gamma are distinct real numbers. The points with position vectors alpha i + beta j + gamma k , beta i + gamma j + alpha k , gamma i + alpha j + beta k

The angle between the lines (x^(2)+y^(2))sin^(2)alpha=(x cos beta-y sin beta)^(2) is

If alpha, beta, gamma are the roots of the equatiion x^(3)-px^(2)+qx-r=0 find (i) sumα^(2) (ii) sumalpha^(2) beta