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Magnitude of the resultant C when doubling B makes the new resultant perpendicular to A

The same question, asked 2 times: 19 Apr 2025 S2, 12 May 2026 S2. Every wording below, oldest first.

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  1. Question 1

    19 Apr 2025 S2

    1
    The resultant of two vectors A→\overrightarrow{A} and B→\overrightarrow{B} is C→\overrightarrow{C}. If the magnitude of B→\overrightarrow{B} is doubled, the new resultant vector becomes perpendicular to A→\overrightarrow{A}, then the magnitude of C→\overrightarrow{C} is

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  2. Question 2

    12 May 2026 S2

    102
    The resultant of two vectors A⃗\vec{A} and B⃗\vec{B} is C⃗\vec{C}. If the magnitude of B⃗\vec{B} is doubled, the new resultant vector becomes perpendicular to A⃗\vec{A}. Then the magnitude of C⃗\vec{C} is

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