Let a=j-k and c=i-j-k. Then the vector b satisfying a×b+c=0 and a.b=3 is

a×b=-c ⇒ a×(a×b)=c×a3a-2b=c×a ⇒ 2b=3a-c×a2b=3j−3k−2i−j−k ,here c×a=2i+j+kb=-i+j-2k

Let a=j-k and c=i-j-k. Then the vector b satisfying a×b+c=0 and a.b=3 is

a×b=-c ⇒ a×(a×b)=c×a3a-2b=c×a ⇒ 2b=3a-c×a2b=3j−3k−2i−j−k ,here c×a=2i+j+kb=-i+j-2k

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Let $a = j - k$ and $c = i - j - k .$ Then the vector $b$ satisfying $a \times b + c = 0 and a . b = 3$ is

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$i + j - 2 k$

$- i + j - 2 k$

$i - j - 2 k$

$2 i - j + 2 k$

answer is A.

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Detailed Solution

$\begin{array}{rcl} a \times b & = & - c \Rightarrow a \times (a \times b) = c \times a \\ 3 a - 2 b & = & c \times a \Rightarrow 2 b = 3 a - c \times a \\ 2 b & = & 3 j - 3 k - 2 i - j - k, h e r e c \times a = 2 i + j + k \\ b & = & - i + j - 2 k \end{array}$