Given that the vectors `alpha` and `beta` are non-collinear. The values of `x` and `y` for which `vecu - vecv = vecw` holds true if `vecu = 2 xalpha + ybeta, vec v = 2yalpha + 3xbeta` and `vecw = 2alpha - 5 beta` are

Given that the vector alpha and beta are non-collinear. The value of x and y for which u-v=w holds true if u= 2 x alpha + y beta, v= 2 y alpha + 3 x beta and w= 2alpha -5 beta , are

If bara and barb are non-collinear vectors, then the value of alpha for which the vectors vecu=(alpha-2)veca+vecb and vecv=(2+3alpha)veca-3vecb are coolinear is :

If vec a and vec b are non-collinear vectors,then the value of x for which vectors vec alpha=(x-2)vec a+vec b and vec beta=(3+2x)vec a-2vec b are collinear,is given by

If vec a and vec b are non-collinear vectors,find the value of x for which the vectors vec alpha=(2x+1)vec a-vec b and vec beta=(x-2)vec a+vec b are collinear.

If vec alpha and vec beta are non-collinear vectors and vec a=(x+4y) vec alpha+ (2x+y+1) vec beta and vec b= (y-2x+2) vec alpha + (2x-3y-1) beta , find x and y so that 3 vec a= 2 vec b .

If vec(a) and vec(b) are non-collinear vectors find the value of x for which vectors vec(alpha)=(x-2)vec(a)+vec(b) and vec(beta)=(3+2x)vec(a)-2vec(b) are collinear.

Let alpha = (lambda-2) a + b and beta =(4lambda -2)a + 3b be two given vectors where vectors a and b are non-collinear. The value of lambda for which vectors alpha and beta are collinear, is.

Let alpha = (lambda-2) a + b and beta =(4lambda -2)a + 3b be two given vectors where vectors a and b are non-collinear. The value of lambda for which vectors alpha and beta are collinear, is.

vecu, vecv and vecw are three nono-coplanar unit vectors and alpha, beta and gamma are the angles between vecu and vecu, vecv and vecw and vecw and vecu , respectively and vecx , vecy and vecz are unit vectors along the bisectors of the angles alpha, beta and gamma. respectively, prove that [vecx xx vecy vecy xx vecz vecz xx vecx) = 1/16 [ vecu vecv vecw]^(2) sec^(2) alpha/2 sec^(2) beta/2 sec^(2) gamma/2 .

vecu, vecv and vecw are three nono-coplanar unit vectors and alpha, beta and gamma are the angles between vecu and vecu, vecv and vecw and vecw and vecu , respectively and vecx , vecy and vecz are unit vectors along the bisectors of the angles alpha, beta and gamma. respectively, prove that [vecx xx vecy vecy xx vecz vecz xx vecx) = 1/16 [ vecu vecv vecw]^(2) sec^(2) alpha/2 sec^(2) beta/2 sec^(2) gamma/2 .