Question

Assertion :Let $|\overrightarrow{a}|=|\overrightarrow{b}|=|\overrightarrow{c}|=1$ such that $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0}$ then $\overrightarrow{a}.\overrightarrow{b}+\overrightarrow{b}.\overrightarrow{c}+\overrightarrow{c}.\overrightarrow{a}=\frac{-3}{2}$ Reason: $(\overrightarrow{p}+\overrightarrow{q}{)}^2=|\overrightarrow{p}{|}^2+|\overrightarrow{q}{|}^2+2\overrightarrow{p}.\overrightarrow{q}$

• A. Both Assertion & Reason are individually true & Reason is correct explanation of Assertion
• B. Both Assertion & Reason are individually true but Reason is not the correct explanation of Assertion
• C. Assertion is true but Reason is false
• D. Assertion is false but Reason is true

Answer 1

The correct option is A Both Assertion & Reason are individually true & Reason is correct explanation of Assertion

Given

$\left|\overline{a}\right|=\left|\overline{b}\right|=\left|\overline{c}\right|=1$

$\overline{a}+\overline{b}+\overline{c}=\overline{0}$

So,
${(\overline{a}+\overline{b}+\overline{c})}^2=0$
$\Rightarrow {\left|\overline{a}\right|}^2+{\left|\overline{b}\right|}^2+{\left|\overline{c}\right|}^2+2(\overline{a}\cdot \overline{b}+\overline{b}\cdot \overline{c}+\overline{c}\cdot \overline{a})=0$
$\Rightarrow \overline{a}\cdot \overline{b}+\overline{b}\cdot \overline{c}+\overline{c}\cdot \overline{a}=\frac{-3}{2}$

Assertion$\left(A\right)$ and Reason$\left(R\right)$ both are true and Reason$\left(R\right)$ is feasible explanation of a Assertion$\left(A\right)$