Evaluate the product (3a-5b) (2a+7b). - Vidyadip

Question

Evaluate the product $\big(3\vec{a}-5\vec{b})\cdot\big(2\vec{a}+7\vec{b}).$

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Answer

$\text{Given:}\ \ \ \ \big(3\vec{a}-5\vec{b}\big).\big(2\vec{a}+7\vec{b}\big)$ $=\big({3\vec{a}\big)}.\big(2\vec{a}\big)+\big(3\vec{a}\big).\big(7\vec{b}\big)-\big(5\vec{b}\big).\big(2\vec{a}\big)-\big(5\vec{b}\big).\big(7\vec{b}\big)$$=6\vec{a}.\vec{a}+21\vec{a}.\vec{b}-10\vec{b}.\vec{a}-35\vec{b}.\vec{b}$
$=6\big|\vec{a}\big|^2+21\vec{a}.\vec{b}-10\vec{a}.\vec{b}-35\Big|\vec{b}\Big|^2$
$=6\big|\vec{a}\big|^2+11\vec{a}.\vec{b}-35\Big|\vec{b}\Big|^2$

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