[" 67.If "|vec alpha+vec beta|=|vec alpha-vec beta|," then: "],[[" (a) "alpha" is parallel to "vec beta," (b) "vec alpha" is perpendicular to "vec beta],[" (c) "alpha=(1)/(2)vec beta,],[" (d) angle between "vec alpha" and "vec beta" is "(pi)/(3)]]

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

| vec alpha + vec beta | = | vec alpha-vec beta |, then (A) vec alpha is parallel to vec beta (B) vec alpha is perpendicular to vec beta (C) | vec alpha | = | vec beta | (D) none of these

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

Given that (vec beta-vec alpha) * (vec beta + vec alpha) = 8 and vec alpha * vec beta = 2 Also | vec alpha | = 1 then angle between (vec beta-vec alpha) and (vec beta + vec alpha) is

If alpha and beta are two nonzero and different vectors such that |vec alpha + vec beta| = |vec beta - vec alpha| then the angle between the vectors vec alpha and vec beta is

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 -

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

If vec(alpha) and vec (beta) are perpendicular to each other , show that | vec(alpha) + vec(beta)|^(2) = |vec(alpha)-vec(beta)|^(2)

Prove that vec R+([vec R*(vec beta xx(vec beta xxvec alpha))]vec alpha)/(|vec alpha xxvec beta|^(2))+([vec R*(vec alpha xx(vec alpha xxvec beta))]vec beta)/(|vec alpha xxvec beta|^(2))=([vec Rvec alphavec beta](vec alpha xxvec beta))/(|vec alpha xxvec beta|^(2))

If vec(alpha) and vec (beta) are perpendicular to each other , show that |vec(alpha)+vec(beta)|^(2) = | vec(a)|^(2) + |vec(beta)|^(2)