If $b = 4 i + 3 j$ and $c$ be two perpendicular vectors in xy-plane. The vector in the same plane having components 1, 2 along $b$ and $c$ respectively, is

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$2 i - j$

$2 i + j$

$i - 2 j$

$i + 2 j$

answer is A.

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Detailed Solution

$b = 4 i + 3 j c = 3 i - 4 j let a = xi + yj \frac{4 x + 3 y = 1}{5} \Rightarrow 4 x + 3 y = 5 \Rightarrow x = 2 y = - 1 \frac{3 x - 4 y}{5} = 2 \Rightarrow 3 x - 4 y = 10$

$\bar{a} = 2 i - j$

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