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If \vec{a}_{1},\vec{a}_{2},\vec{a}_{3},  are non- coplanar vectors and

\left ( x+y-3 \right )\vec{a}_{1}+\left ( 2x-y+2 \right )\vec{a}_{2}+\left ( 2x+y+\lambda \right )\vec{a}_{3}=\vec{0}

holds for some 'X' and 'y' then value of  ' 3\lambda ' is

Option: 1 7

Option: 2 6

Option: 3 -10

Option: 4 5

Answers (1)

best_answer

Since \vec{a}_{1},\vec{a}_{2},\, and\, \, \vec{a_{3}}  are non co planar vectors

\therefore x+y-3=0...............(i)

2 x-y+2=0...............(ii)

2 x+y+\lambda =0...............(iii)

From (i) & (ii) x=1/3, y=8/3

\therefore \, \, From (iii)\lambda = -\frac{10}{3}\Rightarrow 3 \lambda =-10 

 

Posted by

sudhir.kumar

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