`veca and vecb` are two non-collinear vectors. Show that the points with position vectors `l_1 veca+m_1 vecb,l_2 veca+m_2 vecb,l_3 vecb ` are collinear if `|(1,1,1),(l_1,l_2,l_3),(m_1,m_2,m_3)|=0`

If vec a and vec b are two non-collinear vectors, show that points l_1 vec a+m_1 vec b ,l_2 vec a+m_2 vec b and l_3 vec a+m_3 vec b are collinear if |(l_1,l_2,l_3),(m_1,m_2,m_3),( 1, 1, 1)|=0.

bara and barb are two non-collinear vectors that the points with position vectors l_1bara+m_1bar,l_2bara+m_2barb,l_2bara=m_3 barb . Are collinear then find the value of |:(1,1,1),(l_1,l_2,l_3),(m_1,m_2,m_3):|

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 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 vec aa n d vec b are two non-collinear vectors, show that points l_1 vec a+m_1 vec b ,l_2 vec a+m_2 vec b and l_3 vec a+m_3 vec b are collinear if |l_1l_2l_3m_1m_2m_3 1 1 1|=0.

Shown that the points with position vectors veca-2vecb+3vecc,-2veca+3vecb+2vecc and -8veca+13vecb are collinear.

If vec aa n d vec b are two non-collinear vectors, show that points l_1 vec a+m_1 vec b ,l_2 vec a+m_2 vec b and l_3 vec a+m_3 vec b are collinear if |l_1 l_2 l_3 m_1m_2m_3 1 1 1|=0.

If vec a and vec b are two non-collinear vectors, show that points l_(1)vec a+m_(1)vec b,l_(2)vec a+m_(2)vec b and l_(3)vec a+m_(3)vec b are collinear if det[[l_(1),m_(2),l_(3)m_(1),m_(2),m_(3)1,1,1]]=0

If veca and vecb are two non collinear unit vectors and |veca+vecb|= sqrt3 , then find the value of (veca- vecb)*(2veca+ vecb)