If ` vec alpha+vec beta + vec gamma=0`,prove the given equation

vec vec alpha + vec beta + vec gamma = 0, provet vec vec alphavec beta = vec betavec x gamma = vec gamma xvec alpha

If vec alpha, vec beta, vecgamma be three unit vectors such that |vec alpha+vec beta+vec gamma|=1 and vec alpha is perpendicular to vec beta while vec gamma makes angles theta and phi with vec alpha and vec beta respectively, then the value of cos theta+cos phi is -

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

If |vec alpha + vec beta |=| vec alpha - vec beta|, then :

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

Let a be a real number and vec alpha = hati +2hatj, vec beta=2hati+a hatj+10 hatk, vec gamma=12hati+20hati+a hatk be three vectors, then vec alpha, vec beta and vec gamma are linearly independent for :

Let a be a real number and vec alpha = hati +2hatj, vec beta=2hati+a hatj+10 hatk, vec gamma=12hati+20hatj+a hatk be three vectors, then vec alpha, vec beta and vec gamma are linearly independent for :

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 vec alpha|(vec beta xxvec gamma), then (vec alpha xx beta)*(vec alpha xxvec gamma) equals to |vec alpha|^(2)(vec beta*vec gamma) b.|vec beta|^(2)(vec gamma*vec alpha) c.|vec gamma|^(2)(vec alpha*vec beta) d.|vec alpha||vec beta||vec gamma|

If vec(alpha), vec(beta),vec(gamma) are three non-collinear unit vectors such that vec(alpha)+2vec(beta)+3vec(gamma) is collinear with vec(beta)+vec(y) and vec(alpha)+2vec(beta) is collinear with vec(beta)-vec(gamma) , then 2vec(alpha).vec(beta)+6vec(alpha).vec(gamma) +3vec(beta).vec(gamma) equal to