If and are mutually perpendicular vectors, and , then find the value of .
If $\vec{a}$ and $\vec{b}$ are mutually perpendicular vectors, $|\vec{a} + \vec{b}| = 13$ and $|\vec{a}| = 5$, then find the value of $|\vec{b}|$.
Answer
Answer
AIWritten by AI (gemini-2.5-pro) - it can contain mistakes.
Since $\vec{a}$ and $\vec{b}$ are mutually perpendicular, $\vec{a} \cdot \vec{b} = 0$.
$|\vec{a} + \vec{b}|^2 = |\vec{a}|^2 + |\vec{b}|^2 + 2(\vec{a} \cdot \vec{b})$
$13^2 = 5^2 + |\vec{b}|^2 + 0$
$169 = 25 + |\vec{b}|^2 \implies |\vec{b}|^2 = 144 \implies |\vec{b}| = 12$.
From ISC 2026 Mathematics Paper 1, question 16(ii).