If \( \ |\vec{a}|\ =2,\ |\vec{b}|\ =3 \) and \( |2\vec{a}-\vec{b}|=5 \), then \( |2\vec{a}+\vec{b}| \) equals to
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 5
Squaring the given modulus:
\( |2\vec{a}-\vec{b}|^2=4|\vec{a}|^2+|\vec{b}|^2-4\,\vec{a}\cdot\vec{b} \)
\( 16+9-4\,\vec{a}\cdot\vec{b}=25 \)
\( \vec{a}\cdot\vec{b}=0 \)
Then
\( |2\vec{a}+\vec{b}|^2=16+9+4\,\vec{a}\cdot\vec{b} \)
\( =25 \)
\( |2\vec{a}+\vec{b}|=5 \)