Let $x,$ $y,$ and $z$ be real numbers such that $x^2 + y^2 + z^2 = 1.$  Find the maximum value of
\[3x + 4y + 12z.\]
Question:
Let $x,$ $y,$ and $z$ be real numbers such that $x^2 + y^2 + z^2 = 1.$  Find the maximum value of
\[3x + 4y + 12z.\]
Answer:
Let's think step by step.

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13
Let $x,$ $y,$ and $z$ be real numbers such that $x^2 + y^2 + z^2 = 1.$  Find the maximum value of
\[3x + 4y + 12z.\]
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