If `cosalpha, cosbeta, cosgamma` be the direction cosines of a line, prove that `sin^(2)alpha+sin^(2)beta+sin^(2)gamma=2`.

STATEMENT-1 : The angle between the lines whose direction ratios are (1, 2, 3) and (-12, 3, 2) is 90^(@) STAEMENT-2 : The direction cosines of a line whose direction ratios are (3, 4, 12) are (3/13, 4/13, 12/13) . STATEMENT-3 : If cosalpha, cosbeta,cosgamma are the direction cosines of a line then sin^(2)alpha + sin^(2)beta +sin^(2)gamma = 2.

If cos alpha, cos beta, cos gamma are the direction cosines of a line then the value of sin^(2) alpha + sin^(2) beta + sin^(2) gamma is__________

If cosalpha, cosbeta and cosgamma are the direction cosine of a line, then find the value of cos^2alpha+(cosbeta+singamma)(cosbeta-singamma) .

If cos alpha,cos beta,cos gamma are the direction cosine of a line,then find the value of cos^(2)alpha+(cos beta+sin gamma)(cos beta-sin^(2)gamma

If alpha, beta, gamma are direction angles of a line l, then prove that cos^(2)alpha+cos^(2)beta+cos^(2)gamma=1 . Hence, deduce that sin^(2) alpha + sin^(2) beta + sin^(2) gamma = 2 .

If cosalpha,cosbeta,cosgamma are the direction cosines of a vector veca , then cos2alpha+cos2beta+cos2gamma is equal to

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

If cos alpha + cos beta+ cos gamma = 0 = sin alpha + sin beta+sin gamma show that sin^(2)alpha + sin^(2) beta + sin^(2) gamma =cos^(2)alpha +cos^(2) beta + cos^(2) gamma =3/2

If a vector makes angles alpha,beta,gamma with OX, OY and OZ respectively, prove that sin^(2)alpha+sin^(2)beta+sin^(2)gamma=2

If alpha,beta,gamma are the angles which a line makes with OX,OY and OZ , then sin^(2)alpha + sin ^(2) beta+ sin^(2) gamma