‹ Back to the paper
Solve the following.
If a⃗ and b⃗ are mutually perpendicular vectors, |a⃗ + b⃗| = 13 and |a⃗| = 5, then find the value…
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
$\vec{a}\perp\vec{b} \Rightarrow \vec{a}\cdot\vec{b} = 0$.
$|\vec{a}+\vec{b}|^2 = |\vec{a}|^2 + |\vec{b}|^2 + 2\vec{a}\cdot\vec{b} \Rightarrow 169 = 25 + |\vec{b}|^2$.
$|\vec{b}|^2 = 144 \Rightarrow |\vec{b}| = 12$.
Final answer: 12