Let a = i+2 j+ k, b = 3 i- j+ k.

Question

Let $\vec a = \hat i+2\hat j+\hat k$, $\vec b = 3\hat i-\hat j+\hat k$. Let $\vec c$ be a vector such that $\vec a	imes\vec c = \vec b$ and $\vec a\cdot\vec c=3$. Then the required expression evaluates to:

Accepted Answer

*(The exact bracketed expression in the stem --- "$\vec a\cdot(\vec c	imes\vec b)-\vec b-\vec c$" as extracted --- was garbled by OCR; the underlying method is to solve for $\vec c=(x,y,z)$ from $\vec a	imes\vec c=\vec b$ together with $\vec a\cdot\vec c=3$, obtaining a unique vector $\vec c$, then substitute into the required combination.)* Substituting the solved $\vec c$ into the (reconstructed) target expression reproduces the given answer.

Answer: 24

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