The equation of the plane which makes with coordinate axes, a triangle with its centroid `(alpha, beta , gamma)` is

Find the equation of a plane which meets the axes in A ,Ba n dC , given that the centroid of the triangle A B C is the point (alpha,beta,gamma)

If alpha,beta,gamma be the angles which a line makes with the coordinates axes, then

If alpha, beta, gamma are the angles which a line makes with the coordinate axes ,then (A) sin^2alpha=cos^2beta+cos^2gamma (B) cos^2alpha+cos^2beta+cos^2gamma=2 (C) cos^2alpha+cos^2beta+cos^2gamma=1 (D) sin^2alpha+sin^2beta=1+cos^2gamma

The equation of plane parallel to the plane x+y+z=0 and passing through (alpha, beta, gamma0 is (A) x+y+z=alpha+beta+gamma (B) x+y+z=alphabeta+betagamma+gammaalpha (C) x+y+z+alpha+beta+gamma=0 (D) none of these

Let x-ysin alpha-zsin beta=0 , xsin alpha+zsin gamma-y=0 and xsin beta+ysin gamma-z=0 be the equations of the planes such that alpha+beta+gamma=pi//2 (where alpha,beta and gamma!=0)dot Then show that there is a common line of intersection of the three given planes.

If a line makes anles alpha, beta, gamma with the coordinate axes, porve that sin^2alpha+sin^2beta+sin^2gamma=2

If a plane meets the coordinates axes at A, Band C, in such a way that the centroid of Delta ABC is at the point (1,2,3) , the equation of the plane is

A variable plane is at constant distance 3 from origin and meets the axis in X,Y,Z planes through X,Y,Z parallel to coordinate planes are made. If P be the point of intersection of above made planes, given P(alpha, beta, gamma) then (alpha beta gamma)/(sqrt(alpha^(2)beta^(2)+beta^(2)gamma^(2)+gamma^(2)alpha^(2)))=?

If a line makes angles alpha, beta, gamma when the positive direction of coordinates axes, then write the value of sin^(2) alpha + sin^(2) beta + sin^(2) gamma .

If alpha , beta , gamma are the roots of the equation x^3 +px^2 + qx +r=0 then the coefficient of x in cubic equation whose roots are alpha ( beta + gamma ) , beta ( gamma + alpha) and gamma ( alpha + beta) is