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.`

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 unit vectors such that | vec a+ vec b|=sqrt(3), find (2 vec a-5 vec b). (3 vec a+ vec b) .

If vec a\ a n d\ vec b are two non collinear unit vectors such that | vec a+ vec b|=sqrt(3),\ find \ (2 vec a-5 vec b). (3 vec a+ vec b)

Statement -1 : If veca and vecb are non- collinear vectors, then points having position vectors x_(1) vec(a) + y_(1) vec(b) , x_(2)vec(a)+ y_(2) vec(b) and x_(3) veca + y_(3) vecb are collinear if |(x_(1),x_(2),x_(3)),(y_(1),y_(2),y_(3)),(1,1,1)|=0 Statement -2: Three points with position vectors veca, vecb , vec c are collinear iff there exist scalars x, y, z not all zero such that x vec a + y vec b + z vec c = vec 0, " where " x+y+z=0.

If vec a and vec b are two non-collinear vectors having the same initial point. What are the vectors represented by vec a+ vec b and vec a- vec b .

If vec a and vec b are two non-collinear vectors having the same initial point. What are the vectors represented by vec a+ vec b and vec a- vec b .

Vectors vec a and vec b are non-collinear. Find for what value of n vectors vec c=(n-2) vec a+ vec b and vec d=(2n+1) vec a- vec b are collinear?

If vec a and vec b be two non-collinear unit vector such that vec axx( vec axx vec b)=1/2 vec b , then find the angle between vec a and vec b .

If vec a , vec b are two non-collinear vectors, prove that the points with position vectors vec a+ vec b , vec a- vec b and vec a+lambda vec b are collinear for all real values of lambdadot

If vec a , vec b are two non-collinear vectors, prove that the points with position vectors vec a+ vec b , vec a- vec b and vec a+lambda vec b are collinear for all real values of lambdadot