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.`

Explanation

Given,

`A=l_1​ veca+m_1 vec​b`


`B=l_2 vec​a+m_2 vec​b`


`C=l_3 vec​a+m_3 vec​b`

So,

`AB=(l1_​−l_2​)veca+(m_1​−m_2​)vecb`

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