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can you eat potatoes that have sprouted - Simpleprint

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 Question: Find the vector $ \mathbf{v} $ such that $ \mathbf{v} \times \begin{pmatrix} 1 \\ 0 \\ 2 \end{pmatrix} = \begin{pmatrix} -4 \\ 6 \\ 2 \end{pmatrix} $.

📌 Solution: Let $ \mathbf{v} = \begin{pmatrix} a \\ b \\ c \end{pmatrix} $. The cross product is:

📌 \mathbf{v} \times \begin{pmatrix} 1 \\ 0 \\ 2 \end{pmatrix} = \begin{pmatrix} b(2) - c(0) \\ c(1) - a(2) \\ a(0) - b(1) \end{pmatrix} = \begin{pmatrix} 2b \\ c - 2a \\ -b \end{pmatrix} = \begin{pmatrix} -4 \\ 6 \\ 2 \end{pmatrix}.

📌 This gives the system:

📌 $ 2b = -4 \Rightarrow b = -2 $,

📌 $ c - 2a = 6 $,

📌 $ -b = 2 \Rightarrow b = -2 $ (consistent).

📌 From $ b = -2 $, substitute into 2: $ c = 6 + 2a $. Let $ a $ be a free variable. Choosing $ a = 0 $, then $ c = 6 $. Thus, $ \mathbf{v} = \begin{pmatrix} 0 \\ -2 \\ 6 \end{pmatrix} $. Final answer: $ \boxed{\begin{pmatrix} 0 \\ -2 \\ 6 \end{pmatrix}} $.**Question 1:

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