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JEE MATHEMATICS MCQ: ADDITION OF VECTORS

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Let a⃗,  b→,  c⃗\vec a,\overrightarrow {\;b} ,\;\vec c are three non-coplanar vectors such that r1→=a⃗−b⃗+c⃗,  r2→=b⃗+c⃗−a⃗,  r3→=c⃗+a⃗+b⃗,  r⃗=2a⃗−3b⃗+4c⃗\overrightarrow {{r_1}} = \vec a - \vec b + \vec c,\;\overrightarrow {{r_2}} = \vec b + \vec c - \vec a,\;\overrightarrow {{r_3}} = \vec c + \vec a + \vec b,\;\vec r = 2\vec a - 3\vec b + 4\vec c

If r⃗=λ1r1→+λ2r2→+λ3r3→\vec r = {\lambda _1}\overrightarrow {{r_1}} + {\lambda _2}\overrightarrow {{r_2}} + {\lambda _3}\overrightarrow {{r_3}}, then
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Correct option: B
λ1+λ3=3{\lambda _1} + {\lambda _3} = 3
The correct answer is B. By expressing r⃗\vec r as a linear combination of r1→\overrightarrow {{r_1}}, r2→\overrightarrow {{r_2}}, and r3→\overrightarrow {{r_3}} and solving the resulting system of equations, we find that λ1+λ3=3{\lambda _1} + {\lambda _3} = 3.

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