If `veca,vecb` be two non zero non parallel vectors then show that the points whose position vectors are `p_1veca+q_1vecb,p_2veca+q_2vecb,p_3veca+q_3vecb` are collinear if `|(1,p_1,q_1),(1,p_2,q_2),(1,p_3,q_3)|=0`

If veca,vecb,vecc are non zero and non coplanar vectors show that the following vector are coplanar: 2veca-3vecb+4vecc, -veca+3vecb-5vecc,-veca+2vecb-3vecc

If veca and vecb are non-zero, non parallel vectors, then the value of |veca + vecb+veca xx vecb|^(2) +|veca + vecb-veca xx vecb|^(2) equals

Show that the points having position vectors (veca-2vecb+3vecc),(-2veca+3vecb+2vecc),(-8veca+13vecb) re collinear whatever veca,vecb,vecc may be

If veca and vecb are two non collinear unit vectors and |veca+vecb|=sqrt(3) then find the value of (veca-vecb).(2veca+vecb)

If veca vecb are non zero and non collinear vectors, then [(veca, vecb, veci)]hati+[(veca, vecb, vecj)]hatj+[(veca, vecb, veck)]hatk is equal to

If veca,vecb and vecc are three non-coplanar vectors, then the vector equation vecr-(1-p-q)veca+pvecb+qvecc represents a

If veca and vecb are non zero, non collinear vectors and veca_(1)=lambda veca+3 vecb, vecb_(1)=2veca+lambda vecb, vec c_(1)=veca+vecb . Find the sum of all possible real values of lambda so that points A_(1), B_(1), C_(1) whose position vectors are veca_(1), vecb_(1), vec c_(1) respectively are collinear is equal to.

If veca and vecb are non - zero vectors such that |veca + vecb| = |veca - 2vecb| then

If veca and vecb be two non-collinear unit vectors such that vecaxx(vecaxxvecb)=-1/2vecb ,then find the angle between veca and vecb .

Given that veca and vecb are two non zero vectors, then the value of (veca + vecb) xx (veca-vecb) is,