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Solve the following.
If a⃗ and b⃗ are perpendicular vectors, |a⃗ + b⃗| = 13 and |a⃗| = 5, find the value of |b⃗|.
If $\vec{a}$ and $\vec{b}$ are perpendicular vectors, $|\vec{a} + \vec{b}| = 13$ and $|\vec{a}| = 5$, find the value of $|\vec{b}|$.
Answer
Answer
Since $\vec{a} \perp \vec{b}$, $\vec{a}\cdot\vec{b} = 0$.
$|\vec{a} + \vec{b}|^2 = |\vec{a}|^2 + |\vec{b}|^2 + 2\vec{a}\cdot\vec{b} = |\vec{a}|^2 + |\vec{b}|^2$
$169 = 25 + |\vec{b}|^2 \Rightarrow |\vec{b}|^2 = 144$
Hence $|\vec{b}| = 12$.
Final answer: 12