Question

If $|\vec{a} | = 3, |\vec{b}| = 2, |\vec{c}| = 1$ then the value of $|\vec{a}. \vec{b} + \vec{b} . \vec{c} + \vec{c} . \vec{a}|$ is (given that $\vec{a} + \vec{b} + \vec{c} = 0$)

• A. -7
• B. 7
• C. 14
• D. -14

Answer 1

Answer: (B)

7

Answer 2

$\vec{a} + \vec{b} + \vec{c} = 0$ $\Rightarrow \left(\vec{a} + \vec{b} + \vec{c} \right)^{2} = 0$ $\Rightarrow \left|\vec{a} \right|^{2} + \left|\vec{b} \right|^{2} + \left|\vec{c} \right|^{2} + 2 \left(\vec{a}.\vec{b} + \vec{b}.\vec{c} + \vec{c}.\vec{a}\right) = 0$ $\Rightarrow 9 + 4+1+2 \left(\vec{a}.\vec{b} + \vec{b}.\vec{c} + \vec{c}.\vec{a} \right) = 0$ $\Rightarrow \, \vec{a}.\vec{b} + \vec{b}.\vec{c} + \vec{c}. \vec{a} = 7$