Practicing Success
Practicing Success
CUET Preparation Today
| If \(\vec{a},\vec{b},\vec{c}\) are three unit vectors such that \(\vec{a}+\vec{b}+\vec{c}=0\) then \(\vec{a}\cdot \vec{b}+\vec{b}+\cdot \vec{c}+\vec{c}\cdot \vec{a}\) is equal to |
\(0\) \(1\) \(-3/2\) \(-1\) |
| \(-3/2\) |
| \(\begin{aligned}|\vec{a}+\vec{b}+\vec{c}|^{2}&=0\\ |\vec{a}|^{2}+|\vec{b}|^{2}+|\vec{c}|^{2}+2(\vec{a}\cdot \vec{b}+\vec{b}\cdot \vec{c}+\vec{c}\cdot \vec{a})&=0\\ \vec{a}\cdot \vec{b}+\vec{b}\cdot \vec{c}+\vec{c}\cdot \vec{a}&=-\frac{3}{2}\end{aligned}\) |
