The vector equation of the plane passing through ` vec a ,\ vec b , vec c\ i s\ vec r=alpha vec a+beta vec b+gamma vec c` provided that
a.`alpha+beta+gamma=0` b. `alpha+beta+gamma=1` c. `alpha+beta=gamma` d. `alpha^2+beta^2+gamma^2=1`

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

Unit vectors vec a and vec b are perpendicular, and unit vector vec c is inclined at angle theta to both vec a and vec bdot If vec c = alpha vec a+beta vec b+gamma( vec axx vec b), then a=beta b. gamma^1=1-2alpha^2 c. gamma^2=-cos2theta d. beta^2=(1+cos2theta)/2

If alpha,beta,gamma, in (0,pi/2) , then prove that (s i(alpha+beta+gamma))/(sinalpha+sinbeta+singamma)<1

If cos^(-1) alpha + cos^(-1) beta + cos^(-1) gamma = 3pi , then alpha (beta + gamma) + beta(gamma + alpha) + gamma(alpha + beta) equal to

If alpha,beta and gamma are such that alpha+beta+gamma=0 , then |(1,cos gamma,cosbeta),(cosgamma,1,cos alpha),(cosbeta,cos alpha,1)|

If alpha,beta and gamma are such that alpha+beta+gamma=0 , then |(1,cos gamma,cosbeta),(cosgamma,1,cos alpha),(cosbeta,cos alpha,1)|

If alpha,beta and gamma are such that alpha+beta+gamma=0 , then |(1,cos gamma,cosbeta),(cosgamma,1,cos alpha),(cosbeta,cos alpha,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 + 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) =