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a + 2b collinear with c and b + 3c collinear with a: find a + 2b + 6c

The same question, asked 2 times: 11 May 2023 S2*, 12 May 2024 S2. Every wording below, oldest first.

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  1. Question 1

    11 May 2023 S2

    120
    Let a⃗,b⃗\vec{a},\vec{b}, and c⃗\vec{c} be three non-zero vectors such that no two of these are collinear. If the vector a⃗+2b⃗\vec{a}+2\vec{b} is collinear with c⃗\vec{c} and b⃗+3c⃗\vec{b}+3\vec{c} is collinear with a⃗\vec{a}, then a⃗+2b⃗+6c⃗\vec{a}+2\vec{b}+6\vec{c} equals

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  2. Question 2

    12 May 2024 S2

    144
    If a⃗,b⃗,c⃗\vec{a}, \vec{b}, \vec{c} are three non-zero vectors, no two of them are collinear, a⃗+2b⃗\vec{a}+2\vec{b} is collinear with c⃗\vec{c}, b⃗+3c⃗\vec{b}+3\vec{c} is collinear with a⃗\vec{a}, then a⃗+2b⃗\vec{a}+2\vec{b} is

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