Let \( \vec{a} \) and \( \vec{b} \) be two vectors, such that \( |\vec{a}|=3,\ |\vec{b}|=5 \) and the angle between them is 60°, then the value of \( |\vec{a}+\vec{b}| \) is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 7
By the dot product, \( |\vec{a}+\vec{b}|^2=|\vec{a}|^2+|\vec{b}|^2+2\,\vec{a}\cdot\vec{b} \), so
\( \displaystyle |\vec{a}+\vec{b}|^2=|\vec{a}|^2+|\vec{b}|^2+2|\vec{a}||\vec{b}|\cos 60^\circ \)
\( \displaystyle =9+25+2\times 3\times 5\times\frac{1}{2} \)
\( \displaystyle =49 \)
\( \displaystyle |\vec{a}+\vec{b}|=7 \)